Year 6 sits ICAS Paper D. Six practice maths questions at the Paper D level, from the opening questions to the hard end, where Distinction and High Distinction are decided.
The paperICAS Mathematics Paper D: 40 multiple-choice questions in 60 minutes. ICAS English Paper D: 50 questions in 50 minutes.
WhenSat at school, in the school's sitting window (usually August to September).
AwardsHigh Distinction, Distinction, Credit, Merit and Participation, decided by rank within the year level.
The rampThe questions get harder from start to finish; the last third decides the top awards.
Six practice questions, easy to hard
Try each one before opening the answer: the working shows the step where a wrong answer usually goes wrong.
1 · ICAS Paper D · Mathematics · Warm-up
Noah drew this design with straight lines. One line is red. How many of the black lines are parallel to the red line?
4
2
3
1
Show the answer and the working
Answer: B (2)
Parallel lines go in exactly the same direction and never meet. 2 black lines go in the same direction as the red line; 1 other line slopes almost the same way but would meet it.
Fastest method: Check each line's slope: count how many dots across for each dot up or down, and compare with the red line.
The trap: counting the red line itself, or a line that is nearly (but not exactly) in the same direction
2 · ICAS Paper D · Mathematics · Warm-up
Which of these is the best estimate of the mass of a newborn baby?
3.5 kg
3.5 g
3.5 t
3.5 m
Show the answer and the working
Answer: A (3.5 kg)
3.5 kg is a sensible estimate of the mass of a newborn baby. 3.5 g would be far too small. 3.5 t would be far too big. And m does not measure mass at all.
Fastest method: Picture a unit you know (1 mL is a few drops, 1 L is a big bottle, 1 kg is a bag of sugar, 1 m is a big step) and compare.
The trap: keeping the number but choosing a unit 10 or 1000 times too big or too small, or a unit for a different kind of measure
3 · ICAS Paper D · Mathematics · Middle of the paper
Nina wants to shade one more square so that the design has a line of symmetry. Which square should she shade?
Square A
Square B
Square C
Square D
Show the answer and the working
Answer: A (Square A)
With square A shaded, the design folds onto itself along the diagonal from top right to bottom left. None of the other squares gives any line of symmetry.
Fastest method: Look for a fold line that almost works, and find the one square whose mirror partner is missing.
The trap: testing only vertical and horizontal fold lines when the matching line is a diagonal
4 · ICAS Paper D · Mathematics · Middle of the paper
Three numbers are hidden, one at each corner of a triangle. The number written on each side of the triangle is the sum of the two corner numbers at the ends of that side. The sides show 28, 49 and 25. What is the largest hidden number?
2
26
24
23
Show the answer and the working
Answer: B (26)
Each hidden number is used on two sides, so 28 + 49 + 25 = 102 is twice the total: the three numbers add to 51. Taking away each side in turn gives the numbers 23, 26 and 2.
Fastest method: Add the three side numbers: every corner is counted twice. Halve it for the total, then take away a side to get the corner opposite it.
The trap: forgetting that each corner number is counted twice when the sides are added
5 · ICAS Paper D · Mathematics · The hard end
This is the top view of a model built from cubes. The number in each square tells how many cubes are stacked there. Each drawing below shows columns of cubes from the viewer's left to the viewer's right. Which drawing shows the model as seen by someone standing at the BACK and looking at it?
Drawing A
Drawing B
Drawing C
Drawing D
Show the answer and the working
Answer: D (Drawing D)
From the back, each column of the view is the tallest stack in that line of squares. Walk round to the back: the left-to-right order of the columns is reversed. The heights are 3, 2, 2: drawing D.
Fastest method: For each line of squares you look along, only the tallest stack shows. Then put the lines in the order you would see them from that side.
The trap: drawing the view from the opposite side (left and right swapped), or adding the stacks instead of taking the tallest
6 · ICAS Paper D · Mathematics · The hard end
In a game, every white token has the same value and every black token has the same value. Each token is worth a whole number of points (at least 1), and a black token is worth more than a white token. Two white tokens and five black tokens are worth 51 altogether. Which of these could be the value of one white token and two black tokens?
23
22
20
21
Show the answer and the working
Answer: D (21)
List the whole-number values that make 2 × white + 5 × black = 51 with black bigger than white: white 3, black 9 gives 21. Only 21 appears among the options.
Fastest method: Try each possible value for the cheaper token, keep only the ones that give a whole-number value for the dearer one that is bigger, then work out the new combination.
The trap: using a pair that breaks a condition (a white token worth 0, or a black token worth less than a white one)