Master the Syllabus & Conquer the Exam
Four operations, order of operations, factors, multiples, and rounding off.
Four operations, fractions as part of a set, division of a proper fraction by a whole number.
Four operations, rounding off, multiplying and dividing by 10, 100, 1000.
Expressing fractions/decimals as percentage, percentage of a quantity, discount, GST, and interest.
Equivalent ratios, ratio of three quantities, changing ratios. (Moved to P6 in revised syllabus)
Finding rules and patterns in sequences of numbers or shapes.
Algebraic expressions in one variable, evaluating expressions, and solving simple equations.
Length, mass, volume, time. Conversions between units. 12h and 24h clock.
Square, rectangle, triangle, parallelogram, rhombus, and trapezium.
Volume of cube, cuboid, and liquid. Rate of flow.
Angles on a straight line, at a point, vertically opposite angles. Properties of triangles and quadrilaterals.
Radius, diameter, circumference, area, semi-circle, and quarter circle.
Nets of cubes, cuboids, prisms, and pyramids. (Moved to P4 in revised syllabus)
这里为你精心挑选并设计了 10 道完全符合 PSLE Paper 2 水平的 Heuristics（启发式）模型题。这些题目涵盖了上文提到的常考核心模型（如比例变化、总数/差额不变、分支法、找规律等），并且全部采用 PSLE 典型的长句英文进行包装，非常适合用来训练孩子的“断句、圈关键词与建模”能力。
建议让孩子每天限时完成 2 道，每道题必须在草稿纸上画出 Model 或写出 Unit 比例转化，并死死圈出最后的提问主体。
On a rainy Friday afternoon, Devi and Elijah shared some gaming cards in the ratio of 5 : 3. After Devi lost 24 cards to another friend during recess, the ratio of Devi’s cards to Elijah’s cards became 7 : 6. How many gaming cards did Elijah have?
At a school carnival, Ken and Leo initially had marbles in the ratio of 3 : 5. After Leo gave 42 marbles to Ken, they both had an equal number of marbles. Find the total number of marbles Ken and Leo had altogether.
Mrs Tan is 40 years old and her daughter, Chloe, is 12 years old. In how many years' time will Mrs Tan be twice as old as Chloe?
Siti spent 1/4 of her monthly pocket money on a new school bag. She then spent 1/3 of the remaining money on books and saved the rest. If she saved $108, how much pocket money did Siti have at first?
A fruit seller packed a total of 180 apples and oranges into several identical gift boxes. In each gift box, the ratio of the number of apples to the number of oranges was 2 : 3. An apple costs $0.80 and an orange costs $0.50. Find the total cost of all the fruits in the boxes.
A science quiz consists of 30 multiple-choice questions. For every correct answer, 5 marks are awarded. For every incorrect answer, 2 marks are deducted. Caleb answered all the questions and scored 101 marks. How many questions did Caleb answer correctly?
At a community centre charity event, 2/3 of the number of men was equal to 4/7 of the number of women. There were 45 more women than men at the event. How many people were there at the charity event altogether?
Question Characteristics: The question gives you the total sum of two or more items and the difference between them (e.g., “A and B have $150 altogether. A has $30 more than B.”). It is often disguised inside complex fractions or wordy scenarios in Paper 2.
Key Strategy: "Make them equal."
Always draw a simple bar model (one long bar, one short bar) to instantly see whether to add or subtract the difference.
Here are three classic variants of this problem, ranging from straightforward to typical Paper 2 trickiness.
Q11. Basic Sum & Difference (The Foundation)
Question: Primary 6 Level Up Tuitions printed a total of 428 math worksheets for Booklet A and Booklet B. Booklet A had 56 more worksheets than Booklet B. How many math worksheets were printed for Booklet B?
Q12. Fraction-Disguised Sum & Difference (The Speed Bump)
Question: Caleb and Diana baked 210 chocolate chip cookies for a charity bazaar. Caleb gave away 1/4 of his cookies, and Diana baked another 15 cookies. In the end, they found that they had an equal number of cookies left. How many cookies did Caleb bake at first?
(Hint: Break down the "In the end" stage as an equal block, then find the original difference between them before changes).
Q13. Three-Subject Sum & Difference (The Paper 2 Separator)
Question: Ethan, Fiona, and Gabriel shared a cash prize of $1,250 won at a robotics competition. Ethan received $120 more than Fiona. Gabriel received $85 less than Fiona. How much money did Fiona receive from the cash prize?
Here is exactly how to teach your child to parse these long sentences using models.
Solution to Q11:
Identify the goal: Find Booklet B (Smaller item).
Chunking the data: Total Sum = 428, Difference = 56
The Calculation: If we remove the difference (56) from the total, we are left with two equal blocks of Booklet B.
Answer: 186 worksheets
Solution to Q12:
Model the "End" State:
Reverse to the "Start" State:
Set up the Sum & Difference Equation:
Solution to Q13:
Draw the Model relative to Fiona (since both Ethan and Gabriel are compared to her):
Equalize the blocks: Let's make everyone equal to Fiona's block.
Now, $1,215 represents exactly 3 equal blocks of Fiona's share.
Solve for 1 block:
Answer: $405
Study the pattern of figures made of square tiles and triangular tiles below carefully.
(a) Find the number of triangular tiles in Figure 5.
(b) Find the total number of tiles (squares and triangles) in Figure 100.
(c) Which Figure number has a total of 302 tiles?
The figure below shows a square ABCD with a side length of 14 cm. A quarter circle is drawn inside the square with B as the centre and BA as the radius. Another semicircle is drawn inside the square using BC as the diameter. Find the area of the shaded region. (Take π = 22/7)
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