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Questions Q1.
Ali has x cards. Belinda has twice as many cards as Ali. Charlie has 5 more cards than Ali.
They have a total of 33 cards.
(a) Show that 4x + 5 = 33
(3)
(b) Work out the number of cards Ali has.
.............................................................................................................................................. (2)
Q2.
(a) Solve 4x = 20
x = . . . . . . . . . . . . . . . . . . . . . . (1)
(b) Solve y + 5 = 12
y = . . . . . . . . . . . . . . . . . . . . . . (1)
Q3.
(a) Simplify d + d + d + d
..............................................................................................................................................
(1)
(b) Simplify 3f + 4 – 2f + 6
.............................................................................................................................................. (2)
(a) Simplify 5x + 4y + x – 7y
.............................................................................................................................................. (2)
(b) Solve 7(x + 2) = 7
..............................................................................................................................................
Q5.
(a) Complete the table of values for y = 2x + 3 for values of x from 0 to 5
(2)
(b) On the grid, draw the graph of y = 2x + 3 for values of x from 0 to 5
(2)
(Total for question = 4 marks)
Q6.
(a) Complete the table of values for y = 8 – 2x
(2)
(b) On the grid, draw the graph of y = 8 – 2x for values of x from –1 to 4
(2)
(Total for question = 4 marks)
Q7.
Here are some patterns made from dots.
Pattern number 1 Pattern number 2 Pattern number 3
(a) Draw Pattern number 4 in the space below.
(1)
(b) How many dots are needed for Pattern number 15?
.............................................................................................................................................. (2)
Q8.
Here are some patterns made from sticks.
(a) In the space below, draw Pattern number 4
(1)
(b) Complete the table.
(1)
(c) How many sticks make Pattern number 15?
...........................................................
(1)
Maria wants to work out how many sticks make Pattern number 50
(d) Write down a method she can use.
.............................................................................................................................................
.............................................................................................................................................
.............................................................................................................................................
(1) Q9.
Here are the first four terms of an arithmetic sequence.
5 9 13 17
(a) What is the next term of this sequence?
.............................................................................................................................................. (1)
(b) Write down an expression, in terms of n, for the nth term of the sequence.
.............................................................................................................................................. (2)
Q10.
A shop sells packets of envelopes.
There are 5 envelopes in a small packet. There are 20 envelopes in a large packet. There is a total of T envelopes in x small packets and y large packets.
Write down a formula for T in terms of x and y.
...........................................................
Q12.
Dan, Harry and Regan sell cars.
Dan sells x cars. Harry sells 5 more cars than Dan. Regan sells twice as many cars as Dan.
Write an expression, in terms of x, for the mean number of cars Dan, Harry and Regan sell.
Q13.
Katie has x pets. Agatha has twice as many pets as Katie. Isabel has 3 more pets than Katie.
Write an expression, in terms of x, for the total number of pets that Katie, Agatha and Isabel have.
.............................................................................................................................................. Q14.
Stephanie thinks of a positive number. She squares the number and adds 7 The result is 43
What number did Stephanie think of?
...........................................................
Q15.
On the grid, draw the graph of y = 2x + 3 for values of x from x = –3 to x = 1
Q16.
* Here are the first four terms in a number sequence.
5 8 11 14
Kasey thinks that the number 34 is in this sequence.
Is Kasey correct? You must show how you get your answer.
Q17.
Here are the first four terms of an arithmetic sequence.
(a) Find, in terms of n, an expression for the nth term of this arithmetic sequence.
...........................................................
(2)
(b) Is 121 a term of this arithmetic sequence? You must explain your answer.
.............................................................................................................................................
.............................................................................................................................................
.............................................................................................................................................
(2)
Q18.
(a) Simplify 2a + 4b + 3a – b
.............................................................................................................................................. (2)
(b) Expand 5(m + 2)
.............................................................................................................................................. (1)
(c) Simplify a5 × a4
.............................................................................................................................................. (1)
Q19.
(a) Expand 4(3x + 5)
.............................................................................................................................................. (1)
(b) Expand and simplify 2(x – 4) + 3(x + 5)
.............................................................................................................................................. (2)
(c) Expand and simplify (x + 4)(x + 6)
.............................................................................................................................................. (2)
Q20.
(a) Expand 3(2 + t)
.............................................................................................................................................. (1)
(b) Expand 3x(2x + 5)
.............................................................................................................................................. (2)
(c) Expand and simplify (m + 3)(m + 10)
.............................................................................................................................................. (2)
Q21.
(a) Simplify t + t + t
(1)
(b) Simplify 5 × e × f
(1)
(c) Simplify 3x + 8y + x – 2y
(2)
Q22.
(a) Simplify 4b × 2c
..............................................................................................................................................
(1)
(b) Expand 3(2w – 5t)
.............................................................................................................................................. (2)
(c) Expand and simplify (x + 7)(x – 2)
.............................................................................................................................................. (2)
(Total for Question is 5 marks)
Q23.
(a) Simplify r + r + r + 2r
...........................................................
(1)
(b) Simplify 7 × 2t
...........................................................
(1)
(c) Simplify 6ab − 4ab
...........................................................
(1)
(Total for question = 3 marks)
Q24.
(a) Simplify m + m + m + m + m
.............................................................................................................................................. (1)
(b) Simplify 2p + 7p
.............................................................................................................................................. (1)
(c) Simplify t × w × 4
.............................................................................................................................................. (1)
(Total for Question is 3 marks)
Q25.
(a) Simplify c + c + c
.............................................................................................................................................. (1)
(b) Simplify 2e × 3f
.............................................................................................................................................. (1)
(c) Simplify 9p + 2t – 2p + 3t
.............................................................................................................................................. (2)
(Total for Question is 4 marks)
Q26.
(a) Simplify a + a + a + a
.............................................................................................................................................. (1)
(b) Simplify 3 × c × d
.............................................................................................................................................. (1)
(c) Simplify 3ef + 5ef – ef
.............................................................................................................................................. (1)
(d) Solve 6g = 18
g = . . . . . . . . . . . . . . . . . . (1)
(e) Solve 5h + 7 = 17
h = . . . . . . . . . . . . . . . . . . (2)
Q27.
(a) Simplify 4ab − 3ab
(1)
(b) Simplify x2 + x2 + x2
(1)
(c) Simplify 3x − 2y + x − 3y
(2) Q28.
(a) Simplify h + h + h
(1)
(b) Simplify p × r × 3
(1)
(c) Simplify 5x + 4y – 3x + 3y
(2)
k = 5 m = 3
(d) Work out the value of 2k + 4m
...........................................................
(2)
Q29. (a) Simplify 4x + 3y – x – 4y
(2)
(b) Simplify 2 + 4x – 7x
(1)
(c) Simplify t4 × t7
(1)
(d) Simplify y6 ÷ y2
(1)
Q30.
(a) Solve x + x + x = 6
x = ...........................................................
(1)
(b) Solve t + 5 = 20
t = ...........................................................
(1)
(c) Solve 4y = 36
y = ...........................................................
(1)
(d) Solve f + 5 = 12
f = ...........................................................
(2) Q31.
(a) Solve 3(2p – 5) = 21
p =. . . . . . . . . . . . . . . . . . . . (3)
(b) Solve 9x – 11 = 5x + 7
x = . . . . . . . . . . . . . . . . . . . . (3)
Q32. (a) Solve a + a = 18
a = . . . . . . . . . . . . . . . . . . . . . (1)
(b) Solve b – 4 = 8
b = . . . . . . . . . . . . . . . . . . . . . (1)
(c) Solve 7c = 28
c = . . . . . . . . . . . . . . . . . . . . . (1)
P = 2x + 3y x = 5 y = 4
(d) Work out the value of P.
p = . . . . . . . . . . . . . . . . . . . . . (2)
Q34.
Given x = 4
Work out the value of 2x2 + 7
.............................................................................................................................................. (Total for Question is 2 marks)
Q35.
p = n3 – 5 n = 2
Work out the value of p.
(Total for question = 2 marks)
Q36.
P = 3.5x – y
(a) Work out the value of P when x = 12 and y = 5
.............................................................................................................................................. (2)
(b) Work out the value of P when x = –9 and y = –6
.............................................................................................................................................. (2)
Q37.
Here is a rule to work out the time it takes to cook a piece of meat.
A piece of meat has a weight of 4 kg.
(a) Use the rule to work out the time, in minutes, it takes to cook this piece of meat.
........................................................... minutes
(2)
It takes 192 minutes to cook a different piece of meat.
(b) Work out the weight of this piece of meat.
........................................................... kg
(3)
(Total for question = 5 marks)
38.
The diagram shows a semicircle drawn inside a rectangle.
The semicircle has a diameter of 8 cm. The rectangle is 8 cm by 4 cm.
Work out the area of the shaded region. Give your answer correct to 3 significant figures.
. . . . . . . . . . . . . . . . . . . . . . . . cm2
(Total for Question is 4 marks)
Q39. A circle has a diameter of 140 cm.
Work out the circumference of the circle.
Give your answer correct to 3 significant figures.
........................................................... cm
(Total for Question is 2 marks)
Q40.
* The diagram shows the surface of a pond in the shape of a circle.
The circle has a radius of 120 cm.
Mark wants to put 20 fish into the pond. There needs to be a surface area of 1800 cm2 for each fish.
Show that the surface of the pond is large enough for Mark to put 20 fish into the pond.
Mark Scheme Q1.
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