Algebra questions turn words, patterns and shape puzzles into a rule, and your child finds the rule before doing any arithmetic. Your child is tested at their current year level, and each school selects its own test date.
Patterns, rules and letters that stand for numbers, more than long equations. Algebra is one of the areas Edutest names for its Mathematics test, which covers year-level maths: numbers, measurement, algebra, space and data.
Our questions are written for children in Years 6–7 applying for Year 7 or 8. At that level, the knowledge behind them is number patterns, tables of values and the order of operations. It also covers substituting into an expression and solving simple equations by balancing or undoing each step.
Each question tests whether your child can see the structure. Once the rule is clear, the arithmetic inside it is light, so time spent finding the rule is time well spent.
Read each phrase slowly, because it has one exact meaning and the order of the words sets the order of the working. A child who rushes the reading can do perfect arithmetic on the wrong expression.
Some questions build in stages, as in "Bea has… Cal has…". Ask your child to write each person's expression on its own line before combining them.
Words into algebra
Algebra
Words
Watch for
2p
twice as many as p
It means 2 × p, not p + 2
2p + 5
5 more than twice p
Do the doubling first, then add
b − 3
3 fewer than b
Fewer and less than both mean subtract
n ÷ 2
half of n
Also written n/2
m²
m squared
m times m, not 2 × m
ab
the product of a and b
Product means multiply; sum means add
How should your child find a pattern's rule?
Find how much the pattern grows each time, then fix where it starts. Take the pattern 5, 8, 11, 14: these four steps work for any pattern that goes up by a fixed amount, and the last one turns the rule round to test a number.
Find the step
It goes up by 3 each time, so the rule starts with 3 × n, where n is the term number.
Fix the start
Term 1 is 5, and 3 × 1 is 3, so add 2. The rule is 3 × n + 2.
Check on another term
Term 4: 3 × 4 + 2 = 14. It matches, so the rule is right.
Undo the rule to test a number
Is 50 in the pattern? Take away 2 to get 48, and 48 ÷ 3 = 16, a whole number. So 50 is term 16.
Four worked examples
These four are in the style of Edutest Mathematics and get harder as they go. Each one shows the answer and the working; read them with your child and spot the rule or expression together.
As you read, ask which option looked right at first. If it came from a wrong expression, the slip is in the reading; a right expression with a wrong answer points to the order of operations.
Worked explanation 1
Ari has p stickers. Bea has 5 more than twice as many stickers as Ari. Cal has 3 fewer stickers than Bea. Which expression shows how many stickers Cal has?
AA.
2p + 8
BB.
2p + 2
CC.
2p + 7
DD.
2p − 2
Answer: B
Answer: B (2p + 2)
Twice as many as Ari is 2p, and 5 more makes Bea's number 2p + 5. Cal has 3 fewer than Bea: 2p + 5 − 3 = 2p + 2.
The trap: 2p + 8 tempts children who add the 3 instead of taking it away. 'Fewer' means subtract.
Why the other options are wrong
A (2p + 8): Adds the 3 instead of subtracting it.
C (2p + 7): Doubles (p + 5) to get 2p + 10 for Bea, then takes away 3.
D (2p − 2): Takes away the 5 as well as the 3, giving 2p − 5 + 3.
Worked explanation 2
If m = 6 and n = 4, what is the value of m² − 3n ÷ 2?
AA.
6
BB.
12
CC.
24
DD.
30
Answer: D
Answer: D (30)
Put in the numbers: 6² − 3 × 4 ÷ 2. Squares first: 6² = 6 × 6 = 36. Then multiply and divide from left to right: 3 × 4 = 12, and 12 ÷ 2 = 6. Subtract last: 36 − 6 = 30.
The trap: 12 tempts children who subtract before dividing, working out (36 − 12) ÷ 2. Division comes before subtraction.
Why the other options are wrong
A (6): Reads m² as 2 × m = 12, then works out 12 − 6.
B (12): Subtracts first, then halves: (36 − 12) ÷ 2.
C (24): Leaves out the ÷ 2 and works out 36 − 12.
Worked explanation 3
A number pattern starts 3, 10, 17, 24, … and keeps going in the same way. Which of these numbers will appear in the pattern?
AA.
100
BB.
115
CC.
128
DD.
147
Answer: B
Answer: B (115)
The pattern goes up by 7 each time, starting from 3, so every number in it is 3 more than a multiple of 7 (3 = 0 + 3, 10 = 7 + 3, 17 = 14 + 3). Take 3 from each option and test for 7: 97 no, 112 = 16 × 7 yes, 125 no, 144 no. The answer is 115.
The trap: 147 tempts children because it is in the 7 times table (21 × 7). The pattern's numbers are 3 more than multiples of 7, not multiples of 7.
Why the other options are wrong
A (100): 100 − 3 = 97, which is not a multiple of 7.
C (128): 128 − 3 = 125, which is not a multiple of 7.
D (147): 147 is a multiple of 7, so it is 3 away from the pattern.
Worked explanation 4
Each shape stands for a whole number. ▲ + ▲ + ● = 61 and ▲ + ● + ● = 53. What is the value of ▲ + ●?
AA.
8
BB.
23
CC.
38
DD.
57
Answer: C
Answer: C (38)
Add the two lines together. Between them there are three ▲ and three ●, and they total 61 + 53 = 114. So one ▲ and one ● make 114 ÷ 3 = 38. Check: the lines differ by 61 − 53 = 8, which is ▲ − ●, so ▲ = 23 and ● = 15; then 23 + 23 + 15 = 61 and 23 + 15 + 15 = 53.
The trap: 57 tempts children who add the two totals and halve, as if each line held one ▲ and one ●. Each line has three shapes, so the 114 is three ▲ and three ●.
Why the other options are wrong
A (8): 8 is 61 − 53, which equals ▲ − ●, not ▲ + ●.
B (23): 23 is the value of ▲ on its own.
D (57): Halves 114 instead of dividing it by 3.
Why does the order of operations matter?
Because the same numbers give different answers in a different order. Brackets come first, then powers such as squares, then multiplication and division from left to right, then addition and subtraction. Your child may know this as BODMAS or BIDMAS.
Substitution questions are built to catch a child who works strictly left to right. Have your child write the expression out with the numbers in, then circle the part that comes first.
What traps should your child watch for?
Each trap below gives a wrong option that looks just as tidy as the right one. If your child picks one, name the slip together, then use its check on the next few questions.
Reading fewer as add. Cal has 3 fewer than Bea, so the 3 is subtracted. Adding it gives a neat but wrong option.
Confusing the step with the terms. The pattern 3, 10, 17 goes up in sevens, but its terms aren't multiples of 7. A multiple of 7 among the options is there to tempt.
Dividing by the wrong number. Adding ▲ + ▲ + ● to ▲ + ● + ● gives three of each shape, so the total is shared by 3, not 2.
Rounding to make it fit. If undoing a rule gives a term number that isn't whole, the number isn't in the pattern. Rounding to the nearest term is the trap.
How does algebra link to the rest of the test?
Pattern rules lean on the same multiples as number questions, and shape puzzles are the balancing idea your child will meet in equations later. Quick recall of times tables makes every rule faster to find.
Edutest's Numerical Reasoning test covers series, matrices, arithmetical reasoning and deduction. The same rule-finding habit helps there, in number series and in number matrices, where the rule links the numbers in a grid.
Play "guess my rule": one person thinks of a rule such as "times 3, add 2", and the other calls out numbers until they can name it. The game trains the step-and-start habit with no worksheet.
Tile or matchstick patterns work well too: build the first three figures, then predict the tenth without building it.
In the app, the algebra lesson has an Interactive version and Notes. There are also drills by section and topic; a free account drills the free test's questions, and a paid plan opens the rest.
Four questions show the method; the Mathematics section of Practice test 1 shows whether your child can use it against the clock. Afterwards, results by skill show whether algebra is the area costing marks.
