5 minute mini assessment - Web viewA taxi firm charges £0.50 per mile plus a fixed charge of £2.00 . Write down a formula for the cost

5 Minute Mini Assessment

Equations and Inequalities (1)1. Simplify:

a. 4a + b + 3a - 2b b. 3y x 2y c. 5 x2

20 x

2. Find the value of each expression when a = 3 , b = -5 and c = 2

a. 10a + 10b b. a + c2 c. 10ac

3. Find the speed of a car when it travels 75 miles in 3 hours

4. Expand and simplify:a. 3(x + 1) + 2(x + 4) b. 4(d + 2) -2(3 + d) c. (x + 2)(x + 3)

5. Factorise:a. x2+ 5x b. 7x2 - 21x c. 9x + 12y

6.

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Equations and Inequalities ANSWERS1. Simplify:

a. 4a + b + 3a - 2b b. 3y x 2y c. 5 x2

20 x

7a – b 6y2 x4

2. Find the value of each expression when a = 3 , b = -5 and c = 2

a. 10a + 10b b. a + c2 c. 10ac30 + -50 3 + 4 302= -20 =7 =15

3. Find the speed of a car when it travels 75 miles in 3 hoursSpeed=distance

time

Speed=75miles3hours

= 25 miles per hour

4. Expand and simplify:a. 3(x + 1) + 2(x + 4) b. 4(d + 2) -2(3 + d) c. (x + 2)(x + 3)

3x + 3 + 2x + 8 4d + 8 - 6 -2d x2 + 3x + 2x + 6= 5x + 11 = 2d + 2 = x2 + 5x + 6

5. Factorise:a. x2+ 5x b. 7x2 - 21x c. 9x + 12y

= x(x + 5) = 7x(x – 3) = 3(3x + 4y)

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a. x2+ x2+x b. c ×d ×2c c. 16x3

20 x

2. Find the value of each expression when a = 4 , b = -2 and c = -5

a. 10a + 10b b. a + c2 c. 10ac

3. Find the speed of a car when it travels 126 miles in 3 hours

4. Expand and simplify:a. 3(2 x + 1) + 2(x - 4) b. 4(2-g) -2(2 + g) c. 3(2 – j) -4(j – 3)

5. Factorise:a. 5 x3+ 2x2 b. 12x2 y - 4x c. 9x3 y + 12xy

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Equations and Inequalities (2) ANSWERS1. Simplify:

b. x2+ x2+x b. c ×d ×2c c. 16x3

20 x

2 x2+x 2c2d 4 x2

5


b. 10a + 10b b. a + c2 c. 10ac 40 + -20 4 + 25 40−5 = 20 = 29 = -8

3. Find the speed of a car when it travels 126 miles in 3 hoursspeed=distance

time

speed=1263speed=42mph

4. Expand and simplify:b. 3(2 x + 1) + 2(x - 4) b. 4(2-g) -2(2 + g) c. 3(2 – j) -4(j – 3)6 x + 3 + 2x - 8 8-4g -4 - 2g 6 – 3j -4j + 128 x – 5 4 - 6g 18 – 7j

5. Factorise:b. 5 x3+ 2x2 b. 12x2 y - 4x c. 9x3 y + 12xyx2(5 x+2) 4x¿ – 1) 3xy ¿ + 4)

6.



a. 2g−2a+g+a b. s×t× s2 c. 12x3

2 x


a. 10a + bc b. b + c2 c. 3ab

3. Find the speed of a toy car when it travels 12 metres in 3 seconds

4. Expand and simplify:a. 3(2 x - 1) b. 4 (2−x )+3(x−5) c. x (x2−3 )+x (5− y)

5. Factorise:a. 3 x+ 2x2 b. 12x3 - 4x2 c. 3ab−12a

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b. 2g−2a+g+a b. s×t× s2 c. 12x3

2 x3 g−a b. s3 t c. 6 x2


b. 10a + bc b. b + c2 c. 3ab70 + 12 -3 + 16 21−3= 82 = 13 = -7


3. Find the speed of a toy car when it travels 12 metres in 3 secondsspeed=distance

time

speed=12metres3 seconds

speed=4metres per second

speed=4m /s

4. Expand and simplify:b. 3(2 x - 1) b. 4 (2−x )+3(x−5) c. x (x2−3 )+x (5− y)

6 x - 3 8−4 x+3 x−15 x3−3 x+5x−xy −7−x x3+2x−xy

5. Factorise:b. 3 x+ 2x2 b. 12x3 - 4x2 c. 3ab−12a

x¿+ 2x¿ 4 x2(3 x−1) 3a(b−4)

6.

a) 15 boxes x 8 pens = 120 pens

120 – 31 = 89 pens left

b) (rs )−t=number of pens¿


a. d− f +2d+2 f b. r2×r2×b c. 10x4

2 x

2. Find the value of each expression when a = 2.5 , b = -4 and c = 7

a. 10a + bc b. a + b2 c. 5b2a

3. A toy car travels at 8 m/s for 6 seconds. How far did it travel?


4. Expand and simplify:a. 2(2 x - 1) b. 2(2−x )−3(x−5) c. x (x−2 )+ x(5−x)

5. Factorise:a. 2 x+ x2 b. 12 st−2 s c. x3 - 2x2

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b. d− f +2d+2 f b. r2×r2×b c. 10x4

2 x

3d+ f br 4 5 x3

8. Find the value of each expression when a = 2.5 , b = -4 and c = 7

b. 10a + bc b. a + b2 c. 5b2a

25 + -28 2.5 + 16 −205= -3 = 18.5 = -4

9. A toy car travels at 8 m/s for 6 seconds. How far did it travel?


8=distance6

8 x6=distance48metres=distance

10.Expand and simplify:b. 2(2 x - 1) b. 2(2−x )−3(x−5) c. x (x−2 )+ x(5−x)

4 x−2 4−2x−3 x+15 x2−2 x+5 x−x2

¿19−5 x = 3 x11.Factorise:b. 2 x+ x2 b. 12 st−2 s c. x3 - 2x2

x (2+x) 2 s (6 t−1) x2(x−2)

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Equations and Inequalities (5)1. Simplify/expand and simplify:a. 8 x+2x− y−3 x b. 3 ( x+2 )−5 c. 4 (2−x )+x (3+ y )

2. If F=ma, what's the value of Fwhen m=5 and a=3?

3. A taxi firm charges £0.50 per mile plus a fixed charge of £2.00 . Write down a formula for the cost C of hiring this taxi to travel n miles.

4. Solve:a) x−3=8 b) 2 x+3=8

c) 2=4 x+14 d) 3 x=x+1

5. a) Write an expression for the perimeter of this shape:

c) The perimeter of the shape is 43 cm. Work out the value of x

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x+2 cm

x+3 cmx+3 cm

2 x+5 cm


Equations and Inequalities (5) ANSWERS6. Simplify/expand and simplify:b. 8 x+2x− y−3 x b. 3 ( x+2 )−5 c. 4 (2−x )+x (3+ y )

7 x− y 3 x+1 8−4 x+3 x+xy 8−x+xy

7. If F=ma, what's the value of Fwhen m=5 and a=3?F=maF=5 x3F=15

8. A taxi firm charges £0.50 per mile plus a fixed charge of £2.00 . Write down a formula for the cost C of hiring this taxi to travel n miles.

£2.00 + £0.50 x number of miles

C = 2 + 0.5n9. Solve:d) x−3=8

+3 +3x=8+3x=11

e) 2 x+3=8−3 −3 2 x=8−3 2 x=5

÷2 ÷2x=5÷2 x=2.5

e) 2=4 x+14−14 −142−14=4 x −12=4 x

÷4 ÷4 −12÷4=x −3=x

f) 3 x=x+1−x −x3 x−x=1 2 x=1

÷2 ÷2 x=1÷2 x=0.5

10.a) Write an expression for the perimeter of this shape:x+2+x+3+2x+5+x+3

5 x+13

f) The perimeter of the shape is 43 cm. Work out the value of x5 x+13 = 43

−13 −135 x=43−135 x=30

÷5 ÷5x=30÷5 x=6

Equations and Inequalities (6)1. Simplify/expand and simplify:a. b+a−c+2b−a+3 b. 4 ( x+8 )−3 x c. 3 (5−x )+2(3+2x )

cm

cm cm

cm


2.

3. A plumber charges a £50 call-out fee, plus £20 per hour (h). Write an expression for the total cost the plumber will charge.

a) Solve:b) x−13=−5 c) 3 x+2=14

c) 4 x+2=2x+7 d) 5 x=2(x+1)


The perimeter of the shape is 52 cm. Work out the value of x

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Equations and Inequalities (6) ANSWERS5. Simplify/expand and simplify:b. b+a−c+2b−a+3 b. 4 ( x+8 )−3 x c. 3 (5−x )+2(3+2x )

5 x+2 cm

x cm2 x+3 cm

3 x cm


3b−c+3 4 x+32−3 x 15−3x+6+4 x x+32 21+x

6. F=maF=10×2F=20

7. A plumber charges a £50 call-out fee, plus £20 per hour (h). Write an expression for the total cost the plumber will charge.

£50+£20×hCost (£ )=50+20h

d) Solve:e) x−13=−5

+13 +13x=−5+13x=8

f) 3 x+2=14−2 −23 x=14−2

3 x=12÷3 ÷3x=12÷3

x=4e) 4 x+2=2x+7

−2 −24 x=2 x+7−2

4 x=2 x+5−2 x −2 x2 x=5

x=2.5

f) 5 x=2(x+1)5 x=2 x+2−2 x −2 x5 x−2 x=2

3 x=2÷3 ÷3x=2÷3

x=238. a) Write an expression for the perimeter of this shape:

The perimeter of the shape is 52 cm. Work out the value of x14 x+10cm=52

−10 −10 14 x=52−10 14 x=42 ÷14 ÷14 x=42÷14 x=3

Equations and Inequalities (7)1. Simplify/expand and simplify:

cm

cm cm

cm

cm cm

2 x+3+5x+2+x+2x+2+x+3+3 x cm

14 x+10cm


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

2. A garage charges £60 per mot service, plus £20 per hour (h) for the time taken to fix the car. Write an expression for the total cost the garage will charge

3. Write the inequality shown on the number lines

a. ____________

-2 -1 0 1 2 3 4 5

b. ____________

-2 -1 0 1 2 3 4 5

c. ____________

-2 -1 0 1 2 3 4 5

4. Show the inequality on the number line

a. 1 < x < 6

-1 0 1 2 3 4 5 6

b. -1 < x ≤ 1

-5 -4 -3 -2 -1 0 1 2

c. 0 ≤ x ≤ 4

0 1 2 3 4 5 6 7

5. Solve:a) 2x−5=9 b) 3 x+2=x+7



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Equations and Inequalities (7) ANSWERS7. Simplify/expand and simplify:

5 x+3 cm

4 cm2 x+4 cm

3 x cm


b. b−a+c+2b−a+5 b. 4 (5−x )+8 x c. 3 (4−2 x )+2(3+x) 3b−2a+c+5 20−4 x+8 x 12−6 x+6+2 x 20+4 x 18−4 x

8. A garage charges £60 per mot service, plus £20 per hour (h) for the time taken to fix the car. Write an expression for the total cost the garage will charge

= 60 + 20h

9. Write the inequality shown on the number lines

a. ____x<4________

-2 -1 0 1 2 3 4 5

b. x>−2____________

-2 -1 0 1 2 3 4 5

c. x≤0.5____________

-2 -1 0 1 2 3 4 5

10.Show the inequality on the number line

a. 1 < x < 6

-1 0 1 2 3 4 5 6

b. -1 < x ≤ 1

-5 -4 -3 -2 -1 0 1 2

c. 0 ≤ x ≤ 4

0 1 2 3 4 5 6 7

11.Solve:c) 2x−5=9 d) 3 x+2=x+7

12.a) Write an expression for the perimeter of this shape:


5 x+3 cm

4 cm2 x+4 cm

3 x cm

2 x cm 2 x+3 cm

2 x+4+5 x+3+4+2 x+3+2x+3 x¿14 x+14

¿ x=3

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5 minute mini assessment - Web viewA taxi firm charges £0.50 per mile plus a fixed charge of £2.00 . Write down a formula for the cost