Year 8 Revision Questions

Proportionality1. Give a real life example of two variables that is directly proportioned.

2. When a spring is stretched, the extension, E cm, of the spring is directly proportional to the stretching force, F newtons.

(a) Fill in the blanks.

F 5 8 ?

E 12 ? 15

(b) Sketch a graph of F and E.

3. The quantity, P litres, of paint needed to paint a floor is directly proportional to the area, A m2, of the floor.

Given that P = 5 when A = 40, find

(a) The equation connecting P and A

(b) The value of P when A = 140

4. For each table below, say whether it shows direct proportion, or not. If it shows direct, write down the equation connecting Q and P.

P 4 5 8 20Q 6 7.5 12 30

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F

E

(a)

(c)(b)P 2 4 8 40Q 50 25 12.5 2.5

P 1 5 7 10Q 20 5 4 3

Proportionality 2 (a)

F 5 8 6.25

E 12 19.2 15

(b)

3. (a) A=8 P

(b) P = 17.5

4. (a) Direct proportional, Q=1.5 P

(b) Not direct proportional

(c) Not direct proportional

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E

F

Forming and solving simultaneous equations1. Explain how you can solve simultaneous equations graphically.

2. Explain what the meaning of simultaneous equations is.

3. When will a pair of linear simultaneous equations have no solutions?

4. Solve the simultaneous equation {6 p+3 q=214 p+3 q=19 by method of elimination.

5. Solve the simultaneous equation { 4 p+q=223 p+5 q=25 by method of substitution.

6. Solve the simultaneous equation {4 x+3 y=142 x+ y=5 by method of substitution.

7. Solve the simultaneous equation {2x−3 y=115 x+2 y=18 by method of elimination.

8. A goose lays gold and silver eggs.

A gold egg weights three times as much as a silver egg.

One day she lays 9 gold and 5 silver eggs.

Their total weight is 1200 grams.

How heavy is a gold egg?

9. The lines with equations y=2 x+5 and y=3 x−2 intersect.

(a) Explain why the x- coordinate of the point of intersection can be found by solving the equation 2 x+5=3 x−2.

(b) Find the coordinates of the point of intersection.

10. Use the graph below, solve the simultaneous equation {5x+3 y=133 x+5 y=3

3

3 x+5 y=3

5 x+3 y=13

Forming and solving simultaneous equations1. Draw the two lines on the same axes and find the point of intersection

2. Simultaneous equations are two equations with two unknowns. They are called simultaneous because they must both be solved at the same time.

3. When the two equations are multiple of each other, i.e. the two lines are parallel graphically.

4. p = 1, q = 5

5. p = 5, q = 2

6. x = 0.5 , y = 4

7. x = 4, y = -1

8. 112.5 g

9 (a) The y – coordinate of the point of intersection is the same, so we can equate two equations.

(b) (7, 19)

10. (3.5, -1.5)

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Factorising and Solving Quadratic Equations1. What does quadratic equation mean? Give an example.

2. Multiply out and simplify these.

(a) (n+4)(n+5) (b) (a+5)(a−3) (c) ( p−5)2 (d) (x+6)(x−6)

3. Factorise these expressions.

(a) n2+4 n+3 (b) ) n2+7n+6 (c) ) n2+8n+15

4. Factorise x2−11 x+30.

5. Factorise these.

(a) x2−16 (b) ) x2−6 x−16

6. Solve the equation x2+3 x=0

7. (a) Factorise x2+7 x−30

(b) Hence solve the equation x2+7 x−30

8.(a) Solve the equation x2+2x−15=0

(b) Solve the equation x2−8 x+15=0

(c) Solve the equation x2−100=0

9. The dimensions of a rectangle are shown.

The rectangle has an area of 36 cm2.

(a) Form an equation, in term of x, for the area of the rectangle and show that it can be written in the form x2+5 x−50=0.

(b) Solve the equation in part (a) and hence write down the length and the width of the rectangle.

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X+7

X-2

Factorising and Solving Quadratic Equations1. Quadratic equation is an equation with an x2 term.2. (a) n2+9 n+20 (b) a2+2a−15 (c) p2−10 p+25 (d) x2−36

3. (a) (n+3)(n+1) (b) (n+6)(n+1) (c) (n+5)(n+3)

4. (x−6)(x−5)

5. (a) (x−4)(x+4) (b) (x−8)(x+2)

6. x=0∨x=3

7. (a) (x+10)(x−3)

(b) x=−10∨x=3

8. (a) x=−5∨x=3

(b) x=5∨x=3

(c) x=10∨x=−10

9. (a) ( x+7 ) ( x−2 )=36

x2+5 x−14=36

x2+5 x−50=0

(b) ( x+10 ) (x−5 )=0

x=−10∨x=5

Take the answer x=5, so the length of the rectangle is 12 and the width is 3

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Congruence and similarity

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Congruence and similarity9

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Straight Line Graphs

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Straight Line Graphs1. (a) y: 0,2,4,6,8,10

(b) y: -10,-6,-2,2,6,10 (c) y: 0,0.5,1,1.5,2,2.5

2. (a) y: 7,5,3,1,-1(b) y: 7,6,5,4,3(c) y: 6,4,2,0,-2

3.

4. (a) y=3 x+4(b) y=2 x+5(c) y=x(d) y=3 x−1(e) y=−x+6(f) y=−3 x+2(g) y=4 x−4(h) y=−x+3(i) y=3 x

5.

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6.

7. (a) y=2 x+¿¿(b) y=5 x+¿¿(c) y=−3x+¿¿(d) y=−x+¿¿(e) y=−7x¿

(f) y=−x+¿¿(g) y=¿¿ (any number)(h) y=−2x+¿¿

8. (a) y=3 x+2(b) y=5 x−3(c) y=−2x(d) y=−x−4

(e) y=12

x+5 or y=x2+5

9. (a) y=5 x−4(b) y=−2x+8(c) y=4 x−5

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Pythagoras’ Theorem1. Label the hypotenuse in the following triangle.

2. Calculate the length of the side AB.

3. Calculate the length of the side AC.

4. Calculate the area of the following triangle.

5. Determine whether angle ABC is a right angle. Explain your answer.

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18

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Pythagoras’ Theorem1.

2. 8.96 cm (to 3 s.f.)3. 12.5 cm (to 3 s.f.)4. 72 cm2

5. No. 1.92 + 5.22 is not equal to 6.22

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Trigonometry1. Calculate the value of x. Give your answer to 3 significant

figures.

2. Calculate the value of x. Give your answer to 1 decimal place.

3. Calculate the length of side BC. Give your answer to 3 significant figures.

4. Calculate the value of x. Give your answer to 1 decimal place.

5. The diagram below shows a quadrilateral ABCD. Calculate the length of CD, giving your answer to 3 significant figures.

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Trigonometry1. 27.7 cm2. 48.2o

3. 6.32 cm4. 39.8o

5. 16.5 cm

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Probability and Sample Space1. Two fair dice are rolled together. The numbers on the dice are multiplied to calculate the score.

Complete the table below to show all possible scores.

2. The spinner below is made from an equilateral triangle with three sections of equal size.

The spinner is spun twice, and the numbers are multiplied together to calculate the score.

a. What is the probability of a score of 6?b. What is the probability of a score of 8?c. What is the probability of an even score?

3. Two dice are rolled together, and the two numbers are added together to calculate the score.Calculate the probability of an odd score.

4. Two bags contain three counters each. A counter is taken from each bag, and a score is calculated by adding the two numbers chosen.

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Calculate the probability of scoring 4 or more.

5. The two fair spinners below are spun. The numbers are added together to calculate the scores. Find the probability of scoring an 8.

6.

7.

8.

9.

10.

25

11.

12.

13.

26

14.

15.

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Probability and Sample Space1.

2.a. 2/9b. 0c. 5/9

3. 1/24. 2/35. 1/6

6. (a ) 320

(b ) 1520

(c ) 820

7. 0.68. 0.29. 0.17

10. P (white )= 220

P ( purple )=1320 P (white∨purple )=P ( white )+P( purple) ¿ 2

20+ 13

20

¿ 1520

¿ 34

11. (a) 0.2(b) 8

12. x = 0.25

13. (a ) 112

(b ) 312

(c ) 1112

(d ) 412

14. (a) 0.34(b) 0.41

15. 100

Area and Circumference of Circles1.

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2.

3.

4.

29

5.

30

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Area and Circumference of Circles1. 37.7

2. 20.57

3. 50.27

4. 40.7

5. 30.9

8.

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Volume and Surface Area of CylinderQuestion 1

(a) For the red and yellow cylinders, find the volume. (b) For the green cylinders, find the height.(c) For all cylinders, find the surface area.

Question 2

Question 3

Question 4

Question 5

Question 6

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Volume and Surface Area of Cylinder1. V = 9852

SA = 2638.9

2. V = 628.3

SA = 408.4

3. V=7069

SA= 2985

4. V=8.49

SA = 23.69

5. h = 19.1

SA = 1828.4

6. h=11.9

SA = 399.5

Question 2

V=1357

Question 3

SA = 150.8

Question 4

The curved surface area should be 6 π ×14

Question 5

10 pots

Question 6

h = 20

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Transformations of Objects16. Describe the single transformation which maps triangle A onto triangle B

17. Describe the single transformation which maps shape A onto shape B.

18. Describe the single transformation which maps shape P onto shape Q.

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19. Describe the single transformation which maps shape A onto shape B.

20. Describe the single transformation which maps Triangle T onto Triangle C.

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Transformations of Objects1. Rotation by 180o about the origin (clockwise or anticlockwise)2. Rotation by 90o anticlockwise about the origin (or 270o clockwise)3. Translation by the vector (-6, -1)4. Reflection in the line y = x.

Enlargement with centre (0,0)

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