CORE SKILLS HOMEWORK 1 Name:
Each question 1 mark (unless otherwise stated)
NUMBER
1 a) Work out the value. You must not use a calculator.
i) -4 + 3 ……………………………………………………….. ii) 3 – -1 …………………………………………………………….……….
iii) 2 + 3 × 2 …………………………………………………. iv) -2 × 5 – 3 × 2 ………………………………………………… [2]
v) 15 ÷ -3 …………………………………………………. vi) -7 × -3 ……………………………………………………....……
b i) Write down the sum of 7 and 5 ……………………………………………………………………………………………………………
ii) Work out the difference between 18 and 5 ……………………………………………………………………………………….
iii) Work out the product of 2 and 3 ……………………………………………………………………………………………….
c) Use appropriate workings to find the value of;
i) 46.8 + 183.7 [2] ii) 627 – 482 [2] iii) 65 × 32 [2] iv) 576 ÷ 7 [2]
2 a) Round each value.
i) 15 to the nearest 10 …………………………………. ii) 3987 to the nearest 100 …………………………………………….
iii) 2.629 to 1 d.p. ………………………………………… iv) 4508.7 to 1 s.f. …………………………………………………......
b) Work out an estimate for each calculation.
i) 20.3 × 9.81 …………………………………………… [2] ii) 102.3 ÷ 0.49 ………………………………………………………… [2]
iii) 48.2×10.29.72 ……………………………………………………………………………………………………………………………………… [2]
3 a) Circle the prime numbers in this list 2 1 7 9 20 6 8
b) Write down all of the factors of 20. ………………………………………………………………………………………………… [2]
c) Write the first 5 multiples of 6 ………………………………………………………………………………………………………… [2]
d) Work out i) 52 ………………… ii) 33 ………………… iii) 36 ………………… iv) 364 …………………
e) Work out;
i) the Highest Common Factor of 30 and 42 [2] ii) the Lowest Common Multiple of 6 and 8 [2]
4a) Complete the table to show the equivalent
fractions, decimals and percentages
b) Write 5 as a percentage of 20
…………………………………………………………………..
………………………………………………………………….
5 a) Work out the value. You must not use a calculator.
i) 25+15 ………………………………………………………… ii) 713-113 ……………………………………………………………….
iii) 27×3 ………………………………………………………. iv) 920÷320 ………..…………………………………………………….
v) 3 ÷12 ………………………………………………………… vi) 212÷2 ……………………………………………………………….
b) These fractions show equivalent mixed numbers and improper fractions. Fill in the blanks.
i) 54 ≡1 4 ii) 3 ≡5 13 iii) 277 ≡ (iv) ≡2 12
c) Complete the equivalent fractions. Fill in the blanks.
i) 812 ≡ 3 ≡ 24 ii) 3 ≡159≡25 iii) 2050 ≡100≡1
d) Work out the value. You must show full workings.
i) 23+14 ……………………………………………………….. ii) 138-34 ……………………………………………………………….
……………………………………………………….. [2] ……………………………………………………… [2]
iii) 35×23 ………………………………………………………. iv) 45÷14 ………..…………………………………………………….
……………………………………………………….. [2] ………………………………………………………… [2]
6 a) Calculate (you may use a calculator!)
i) 34 of 12 ………………………………………………………. ii) 12% of 36 ……………………………………………………….
iii) 25 of 74 ………………………………………………………. iv) 6.5% of 123 ……………………………………………………….
b) Write each ratio in its simplest form
i) 4 : 2 …………………………………………………………… ii) 27 : 15 ………………………………………………………………….
c) Share 48 in the ratio 5 : 1 ……………………………………………………………………………………………………… [2]
ALGEBRA
1 a) Count the number of terms and simplify each of the expressions.
i) 3x – 4 + x + 5 Number of terms: ……… …………………………….……………………………………………… [3]
ii) 5 – 2a + 3a × 2 Number of terms: ……… …………………………….……………………………………………… [3]
iii) -3m × 3 – 2b × 4 Number of terms: ……… …………………………….……………………………………………… [3]
b) Multiply out the brackets and simplify if possible;
i) 3(x + 2) [2] ii) 2(x – 2) [2] iii) 3(a + 2) – 2(a – 3) [2]
iv) (x + 2) (x – 3) [2] v) (2x + 1) (x – 2) [2] vi) (x + 3)2 [2]
c) Fully factorise the expressions;
i) 3x + 9 [2] ii) 15a – 10 [2] iii) 7x + 7 [2]
iv) x2 + 7x + 6 [2] v) x2 + 2x – 3 [2]
2) Solve the equations
a) x + 3 = -5 ……………………………………………………………………………………………………………………………………………...
b) 2x – 3 = 4 + x ………………………………………………………………………………………………………………………………… [2]
c) 3x – 1 = 2 – x ………………………………………………………………………………………………………………………………… [2]
d) 3x = 7 ……………………………… e) x3 = 5 …………………………..… f) 2x = 3 ……….…………………………
3) In each of the expressions, s = 2, t = 3 and u = -4. Work out the value of each expression.
a) st ………………………………..… b) u + t …………………..……………. c) us ………………………………………..
4 a)
b)
STATISTICS
1 a) Here is a list of values 2 1 2 8 2 3 3
i) Write down the mode …….……………… ii) Work out the median ………..…………………………………….……….
iii) Work out the range ………………………… iv) Work out the mean ………………………………………………… [2]
v) Work out the inter quartile range (show full workings) ...... ……………………………………………………… [2]
b) Here is a frequency table for discrete data.
c) Here is a grouped frequency table for continuous data.
2) Here is a table providing information about sales of newspapers over a five day period in a shop.
3) The table shows ‘hours of sleep’ and ‘time spent playing computer games’ for a group of 10 students on
a Saturday.
Hours of sleep / 8 / 6.5 / 9 / 5.5 / 7 / 7.5 / 6 / 10 / 8 / 7.5Time spent playing games (mins) / 30 / 60 / 20 / 80 / 60 / 75 / 90 / 20 / 40 / 45
a) Plot the points on the scatter graph and label the axes [2]
[2]
4) Here is a table providing information about eye
colour.
a) Draw a pie chart in the space provided. [5]
(use a pair of compasses and angle measurer or protractor)
b) Write down how many degrees of turn are
used to represent each individual value in the
pie chart; [1]
……………………………………………………………………………
GEOMETRY
1 a) Measure the length of each line segment, AB and AC to the
nearest millimetre and measure the size of angle BAC
Label the diagram clearly with the measurements. [2]
b) Tick the boxes to categorise each of the angles shown.
c) Work out the size of the angles labelled with letters.
a = ……………………………………… b = ………………..……………………….. c = …………………………………………….
………………………………… [1] …………………………………… [2] d = ………………………………………
2 a) Write down the name of each of the shapes shown.
……………………………………………………. /
……………………………………………………. /
…………………………………………………….
……………………………………………………. /
……………………………………………………. /
…………………………………………………….
……………………………………………………. /
……………………………………………………. /
…………………………………………………….
b) Write the letters of the shapes which have exactly 1 line of symmetry …………………………………………..[3]
c) Write the letters of the shapes which have an order of rotational symmetry of 2 …………………………. [2]
3 a) Construct the perpendicular bisector of b) Measure angle RST and label the diagram
line segment MN. Show all construction lines. [2] Construct the bisector of angle RST [2]
4 a) Work out or calculate the perimeter and area for each of the shapes shown. The grids are cm2 grids.
Perimeter = ………………….. Perimeter = ………………….. Perimeter = ……………….. Perimeter = …………….… [2]
Area = ………………………….. Area = …………………….…….. Area = ………………………….. Area = ………………………. [2]
b) The following cuboids have been made from centimetre cubes
Number of cubes on Number of cm3
bottom layer: ……….... on bottom layer: ……….…..
Number of layers: ……….….. Number of layers: ……….…..
Volume = ………….…….. [3] Volume = ………………..…. [3]
c) Work out the area of each of the shapes given they have been drawn on cm2 grids;
Area = ………………… [2] Area = ………………….. [2] Area = …………………… [2] Area = ………………… [2]
5) Draw the net for a cuboid with
a length of 4 cm, a width of 3 cm
and a depth of 2 cm using the cm2
grid provided:
[3]
6 a) Write down the number of metres in 5 kilometres ……………………………………………………………………………
b) Write down the number of millimetres in 3.2 centimetres …………………………………………………………………
c) Write down the number of centimetres in 4.3 metres ……………………………………………………………………….
d) 1 inch = 2.5 centimetres
How many centimetres are in 3.7 inches? ……………………………………………………………………………… [2]
You may use a calculator