Cambridge Essentials Mathematics Core 8 A4 Consolidation Worksheet
/ A4 Consolidation Worksheet1This is an algebra caterpillar.
Each section contains the sum of the two previous sections.
Remember to add like terms andsimplify your expressions.
Complete these algebra caterpillars.
ab
cd
2When multiplying out brackets in an expression remember to multiply all the terms inside the bracket by what is on the outside.
For example,3(p + 2)= 3 × p + 3 × 2 = 3p + 6
Multiply out these brackets.
a2(a + b)b4(2m – n)c5(p + 3q)
3Area of a rectangle = length × width.
The area of this rectangle is 4 × (a + 7).
This is the same as 4(a + 7) and after
multiplying out the brackets it simplifies to 4a + 28.
i Write down an expression with brackets for the areas of these rectangles.
ii Work out the simplified expressions by multiplying out the brackets.
a b c
de
4The distance–time graph shows the distance Jack walked at a constant speed.
aHow far did Jack walk in 5 hours?
bHow far did Jack walk in 1 hour?
This is his speed in kilometres per hour.
cUse your answer to b to complete this
equation that links the distance
Jack walked (d km) and the time he
took (t hours).
d = t
dJack continued to walk at this speed.
Use your equation from part c to
calculate how far Jack walked in 8 hours.
eHow long will it take Jack to walk 45 km?
5This distance–time graph shows the distance Kofi cycled from point 0 at a steady speed.
At the same time thatKofi started cycling, Maisie started walking in the same direction but from a point 20 km from 0.
aHow long did Kofi take to
overtake Maisie?
bHow far had Kofi cycled before
he overtook Maisie?
cWhat was Kofi’s speed in
kilometres per hour?
dWhat was Maisie’s speed in
kilometres per hour?
eWrite an equation that links
the distance (K km) Kofi travelled
from 0 with time (t hours).
fWrite an equation that links the distance (Mkm) Maisie travelled from 0 with
time (t hours).