Stage 9 - Q1 - 2 marks
A number is increased by 10, then multiplied by 2, giving 44. Form and solve an equation for the original number.
Hint
The first operation belongs inside a bracket.
Stage 9 - Q2 - 2 marks
In 5 years, a person will be twice the age they were 2 years ago. Form and solve an equation for their current age.
Hint
Both ages change from the same present age.
Stage 9 - Q3 - 3 marks
The rectangle perimeter is 26 cm. Its labelled lengths are in cm. Find \(x\) and both dimensions.
Hint
Each rectangle dimension is counted twice.
Stage 9 - Q4 - 3 marks
An isosceles triangle has vertex angle \(114^\circ\). Each equal base angle is \((x+7)^\circ\). Find \(x\) and all three angles.
Hint
Count the equal base-angle expression twice.
Stage 9 - Q5 - 4 marks
A triangle has sides \(x+4\), \(x+3\) and \(x+6\) cm. Its perimeter equals that of a rectangle 12 cm by 6.5 cm. Find \(x\) and check the three resulting sides can form a triangle.
Hint
Equal perimeters do not mean corresponding sides are equal.
Stage 9 - Q6 - 4 marks
A triangle has sides \(x+5\), \(x+3\) and \(x+7\) cm. Its perimeter equals that of a rectangle 15 cm by 7.5 cm. Find \(x\) and check the three resulting sides can form a triangle.
Hint
Equal perimeters do not mean corresponding sides are equal.
Stage 9 - Q7 - 5 marks
One group of \(x\) learners shares 72 pencils and gets 6 each. A second group has 3 more learners and shares 120 pencils, getting 8 each. Form both equations and verify one common \(x\).
Hint
The second group size is \(x+3\), not \(x\).
Stage 9 - Q8 - 5 marks
A booking costs USD 22 plus USD 6 per hour. The total is USD 106. Form an equation and find the number of hours.
Hint
The fixed charge is paid once.
Stage 9 - Q9 - 5 marks
One machine multiplies a number by 4 and adds 5. A second multiplies the same number by 2 and adds 13. Their outputs agree. Find the input.
Hint
Both machines receive the same unknown input.
Stage 9 - Q10 - 3 marks
A two-digit positive integer has digit sum 13. Reversing its digits makes a number 27 larger. Form an equation in one digit, find the number and show that its digits are valid.
Hint
The two digits have different place values in the two numbers.