KS3 maths worksheets › Weekly checks › Weekly check: Year 8 part 1 Year 8 · Key Stage 3 · free KS3 maths weekly check Weekly check: Year 8 part 1
20 mixed questions from 8 Year 8 topics, 50 marks. It covers BIDMAS (order of operations) to area and circumference of circles, the first third of the year in the order schools usually teach it.
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The questions
1 A regular hexagon has sides of 7 cm. Work out its perimeter. A regular pentagon has a perimeter of 45 cm. Work out the length of one side. Work out the perimeter of the quadrilateral in the diagram. 7 cm 4.6 cm 5.2 cm 3.9 cm Diagram NOT accurately drawn 3 marks Show answer a) 42 cmb) 9 cmc) 20.7 cm
See the working a ) 6 e q u a l s i d e s
6 × 7 = 4 2
4 2 c m
b ) 5 e q u a l s i d e s
4 5 ÷ 5 = 9
9 c m
c ) A d d a l l t h e s i d e s
7 + 4 . 6 + 5 . 2 + 3 . 9 = 2 0 . 7
2 0 . 7 c m
Show answer 31
See the working R o o t s a n d p o w e r s f i r s t
√ 4 9 + 2 3 × 3 = 7 + 8 × 3 T h e n m u l t i p l y = 7 + 2 4 = 3 1
3 1
3 Write 23 × 24 as a single power of 2 Jamal says, "23 + 24 = 27 ". 3 marks Show answer a) 27 b) 23 + 24 = 8 + 16 = 24, but 27 = 128, so they are not equal
See the working a ) S a m e b a s e , × m e a n s a d d t h e p o w e r s
2 7
b ) W o r k o u t e a c h s i d e
2 4 ≠ 1 2 8 , a d d i n g p o w e r s d o e s n o t a d d t h e i n d i c e s
J a m a l i s w r o n g
4 Write 32 5 Write 29 6 2 marks Show answer a) 17 5 b) 4 5 6
See the working a )
3 × 5 = 1 5
1 5 + 2 = 1 7
1 7 5
b )
2 9 ÷ 6 = 4 r e m a i n d e r 5
4 5 6
5 A rectangle is 12 cm long and 9 cm wide.
A rectangle 5 cm by 4 cm is removed from one corner.
Work out the area of the remaining shape.
12 cm 5 cm 4 cm 9 cm Diagram NOT accurately drawn 3 marks Show answer 88 cm²
See the working F u l l r e c t a n g l e
A = 1 2 × 9 A = 1 0 8 C o r n e r r e m o v e d A = 5 × 4 A = 2 0 R e m a i n i n g = 1 0 8 - 2 0 R e m a i n i n g = 8 8
8 8 c m 2
6 A slice of a round cheese is a sector of a circle with radius 12 cm and angle 75°.
Work out the length of the curved edge (the arc) of the slice. Work out the perimeter of the slice. Give your answers correct to 1 decimal place.
12 cm 75° Diagram NOT accurately drawn 3 marks Show answer a) 15.7 cmb) 39.7 cm
See the working a )
A r c = 7 5 3 6 0 × π × 2 4
= 1 5 . 7 0 . . .
1 5 . 7 c m
b ) A r c + t w o r a d i i
1 5 . 7 0 . . . + 1 2 + 1 2 = 3 9 . 7 0 . . .
3 9 . 7 c m
7 Use your calculator to work out
(2.42 + 1.8) ÷ 0.53
Write down all the figures on your calculator display.
2 marks Show answer 60.48
See the working T o p f i r s t
2 . 4 2 = 5 . 7 6 5 . 7 6 + 1 . 8 = 7 . 5 6 T h e n t h e p o w e r 0 . 5 3 = 0 . 1 2 5 7 . 5 6 ÷ 0 . 1 2 5 = 6 0 . 4 8
6 0 . 4 8
8 A circle has diameter 18 cm.
Work out the circumference of the circle. Give your answer in terms of π. Work out the area of the circle. Give your answer in terms of π. 3 marks Show answer a) 18pi cmb) 81pi cm2
See the working 9 An L-shape is made by removing a rectangle 3 cm by 2 cm from one corner of a rectangle 8 cm by 6 cm.
Work out the perimeter of the L-shape.
8 cm 3 cm 2 cm 6 cm Diagram NOT accurately drawn 3 marks Show answer 28 cm
See the working F i n d t h e m i s s i n g s i d e s
T o p s i d e = 8 - 3 T o p s i d e = 5 c m R i g h t s i d e = 6 - 2 R i g h t s i d e = 4 c m A d d a l l s i x s i d e s P = 8 + 4 + 3 + 2 + 5 + 6 P = 2 8
2 8 c m
10 A number x is 470, correct to 2 significant figures.
Complete the error interval for x .
....... ≤ x < .......
2 marks Show answer 465 ≤ x < 475
See the working 2 s f o f 4 7 0 i s t h e n e a r e s t 1 0
H a l f o f 1 0 i s 5
L o w e r b o u n d = 4 7 0 - 5 L o w e r b o u n d = 4 6 5 U p p e r b o u n d = 4 7 0 + 5 U p p e r b o u n d = 4 7 5
4 6 5 ≤ x < 4 7 5
11 Write 264 as a product of its prime factors.
2 marks Show answer 23 × 3 × 11
See the working D i v i d e b y p r i m e s
2 6 4 ÷ 2 = 1 3 2 1 3 2 ÷ 2 = 6 6 6 6 ÷ 2 = 3 3 3 3 ÷ 3 = 1 1 1 1 i s p r i m e 2 6 4 = 2 × 2 × 2 × 3 × 1 1
2 6 4 = 2 3 × 3 × 1 1
12 Choose the correct symbol, <, > or =, to make each statement true.
3 5 7 10 4 6 2 3 2 marks Show answer a) <b) =
See the working a )
M a k e t h e d e n o m i n a t o r s t h e s a m e
6 1 0 < 7 1 0
3 5 < 7 1 0
b )
÷ 2 t o p a n d b o t t o m
4 6 = 2 3
13 Here is a list of numbers.
6 8 9 16 21 27 28 49 125
From the list, write down
the square numbers the cube numbers the triangle numbers 3 marks Show answer a) 9, 16, 49b) 8, 27, 125c) 6, 21, 28
See the working a ) S q u a r e n u m b e r s
1 , 4 , 9 , 1 6 , 2 5 , 3 6 , 4 9 , . . .
9 , 1 6 , 4 9
b ) C u b e n u m b e r s
1 , 8 , 2 7 , 6 4 , 1 2 5
8 , 2 7 , 1 2 5
c ) T r i a n g l e n u m b e r s : a d d 2 , t h e n 3 , t h e n 4 , . . .
1 , 3 , 6 , 1 0 , 1 5 , 2 1 , 2 8 , 3 6
6 , 2 1 , 2 8
14 Write 600 as a product of its prime factors. Give your answer in index form. Hence write 1200 as a product of its prime factors in index form. 3 marks Show answer a) 23 × 3 × 52 b) 24 × 3 × 52
See the working a )
6 0 0 = 2 × 3 0 0
3 0 0 = 2 × 1 5 0
1 5 0 = 2 × 7 5
7 5 = 3 × 2 5
2 5 = 5 × 5
6 0 0 = 2 × 2 × 2 × 3 × 5 × 5
6 0 0 = 2 3 × 3 × 5 2
b )
1 2 0 0 = 2 × 6 0 0
O n e m o r e 2
1 2 0 0 = 2 4 × 3 × 5 2
15 Work out the missing number in each calculation.
−8 × □ = 56 □ ÷ (−3) = 6 2 marks Show answer a) -7b) -18
See the working a ) U s e t h e i n v e r s e , ÷ b y - 8
C h e c k : - 8 × - 7 = 5 6
- 7
b ) U s e t h e i n v e r s e , × b y - 3
C h e c k : - 1 8 ÷ - 3 = 6
- 1 8
16 A circular coaster has a diameter of 10 cm.
Work out the circumference of the coaster. Work out the area of the coaster. Give each answer correct to 1 decimal place.
3 marks Show answer a) 31.4 cmb) 78.5 cm²
See the working a )
C = π d
C = π × 1 0 = 3 1 . 4 1 5 . . .
3 1 . 4 c m
b ) R a d i u s f i r s t
r = 1 0 ÷ 2 = 5
A = π r 2
A = π × 5 2 = 7 8 . 5 3 9 . . .
7 8 . 5 c m 2
17 Write down the denominator of the fraction 15 35 Write 15 35 Write 24 36 3 marks Show answer a) 35b) 3 7 c) 2 3
See the working a ) D e n o m i n a t o r = t h e b o t t o m n u m b e r
3 5
b ) ÷ 5 t o p a n d b o t t o m
3 7
c ) H C F o f 2 4 a n d 3 6 i s 1 2 , s o ÷ 1 2 t o p a n d b o t t o m
2 3
18 Work out 15 − 6 + 4 Work out 30 ÷ 5 × 3 2 marks Show answer a) 13b) 18
See the working a ) + a n d - a r e e q u a l , g o l e f t t o r i g h t
1 3
b ) × a n d ÷ a r e e q u a l , g o l e f t t o r i g h t
1 8
19 The mass of a cat is 8.3 kg, correct to 1 decimal place.
Complete the error interval for the mass, w kg, of the cat.
....... ≤ w < .......
2 marks Show answer 8.25 ≤ w < 8.35
See the working 1 d p : h a l f o f 0 . 1 i s 0 . 0 5
L o w e r b o u n d = 8 . 3 - 0 . 0 5 L o w e r b o u n d = 8 . 2 5 U p p e r b o u n d = 8 . 3 + 0 . 0 5 U p p e r b o u n d = 8 . 3 5
8 . 2 5 ≤ w < 8 . 3 5
20 Here are the temperatures, in °C, at 6 am on five days in January.
−4 −1 2 −3 −4
Work out the mean temperature.
2 marks Show answer -2°C
See the working A d d t h e m u p
- 4 - 1 + 2 - 3 - 4 = - 1 0 D i v i d e b y h o w m a n y - 1 0 ÷ 5 = - 2
- 2 ° C
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Every question here is original and written by Robinson Tuition, drawn from the Year 8 topic worksheets. It follows the Key Stage 3 programme of study.
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