221 P6.SP.TL.18012281
Level 3
At 8 a.m., Shaira and Joana raced off together from the starting point of a trail. Shaira ran at an average speed of 3 m/s. Joana ran at an average speed of 4 m/s. Upon reaching the end of the trail, Joana rested for 5 minutes. She then immediately ran back along the same route at 4 m/s. At 8.40 a.m., Shaira met Joana.
  1. Find the total distance covered by the two runners when they met each other. Express the answer in km.
  2. Find the length of the trail in km.
4 m
DST triangle Average speed Different speed Same starting point Meeting point Distance apart Unit conversion Duration
222 P6.SP.TL.18012283
Level 3
Singapore and Kuala Lumpur is 375 km apart. Rael left Singapore for Kuala Lumpur at 10.00 a.m. travelling at an average speed of 75 km/h. Sam left Singapore later than Rael and caught up with him at 12.00 p.m. Sam was travelling at a speed of 90 km/h.
  1. At what time did Sam leave Singapore?
  2. How much later did Rael arrive in Kuala Lumpur than Sam?
4 m
DST triangle Different speed Same starting point Different starting time Overtaking Distance apart Duration Start end time Timeline
223 P6.AP.TL.17090773
Level 3
The figure shows a square that is cut out from a big triangle. The area of the triangle and that of the square are whole numbers. Both the height and the base of the triangle are equal. If the shaded area is 73 cm2, find
  1. The length of the square
  2. The base of the triangle
3 m
Length Square Square & square root Triangle Guess & check
224 P6.SP.TL.18012284
Level 3
At 8 a.m., Rina started from City A and travelled towards City B and his speed remained constant throughout. At 9 a.m., Mandy started her journey from City A towards City B at an average speed of 72 km/h. Mandy overtook Rina at 12 p.m. After overtaking, Mandy carried on her journey at the same average speed and reached at City B at 2:30 p.m.
  1. Find Rina's average speed in km/h.
  2. What is the distance between the two cities?
4 m
DST triangle Average speed Same starting point Different starting time Overtaking Duration Start end time Timeline
225 P6.SP.TL.18012285
Level 3
After 20 minutes into a race, Daniel has run 58 of the route while Piolo has covered only 38 of the distance. Daniel runs at the same average speed throughout the race and Piolo's average speed is 60 m/min slower than Daniel's. If Piolo wants to finish the race at the same time as Daniel, by how many percent should he increase his average speed by for the remaining part of the race? Round off the answer to the nearest whole number.
4 m
DST triangle Average speed Different speed Same starting point Direct ratio W Round off Fraction of a whole Percent change to More than or less than
226 P6.SP.TL.18012287
Level 3
Timothy took 15 min to jog from his home to his school. After that, he took 20 min to walk the same way home. His walking speed was 3 km/h slower than his jogging speed.
  1. Find Timothy's jogging speed in km/h.
  2. How far was the school from his home?
4 m
DST triangle Average speed Different speed Distance apart Inverse ratio Unit conversion Duration More than or less than
227 P6.SP.TL.18012275
Level 3
Edward cycled from the mall to the bank at 80 m/min. His sister cycled from the bank to the mall at 65 m/min. Both of them started cycling towards each other at the same time and did not change their speeds throughout their journey. When Edward reached the mall, his sister was 480 m from the bank. What was the distance between the mall and the bank? Express your answer in m.
4 m
DST triangle Average speed Different speed Different starting point Same starting time Common time
228 P6.SP.TL.18012279
Level 3
A pharmacy and a bank, 500 m apart, are situated between Tina's apartment and Lynn's house as shown. The bank is half-way between the two houses. Tina and Lynn left their homes at the same time and arrived at the pharmacy at the same time. Tina drove at a speed of 65 km/h while Lynn drove at a speed 10 km/h slower than Tina.
  1. How much further did Tina travel than Lynn?
  2. How far is Lynn's house from the bank?
4 m
DST triangle Average speed Different starting point Same starting time Distance apart Common time More than or less than
229 P6.SP.TL.18012282
Level 3
Building A and Building B were 360 km apart. A car travelled from Building A towards Building B. At the same time, a bus started from Building B to Building A. After travelling 112 hours, the two vehicles were still 144 km apart. If the ratio of the average speed of the bus to that of the car was 4 : 5, find
  1. the average speed of the bus.
  2. the time taken for them to meet. travelling the rest of the journey
4 m
DST triangle Average speed Different starting point Same starting time Distance apart Direct ratio Common time Duration Units method
230 P6.SP.JC.19090801
Level 3
Kenny and Jerry started on a 50-km cycling trip at the same time. They cycled at the same speed for first 10 km. For the remaining 40 km, Kenny cycled faster than Jerry. He arrived at the finishing point 40 minutes before Jerry who was 10 km behind him. Jerry did not change his speed throughout and completed it at 11 30.
  1. At what time did the trip begin? Give the answer in 12-hour format.
  2. What was Kenny's average speed for the remaining 40 km of the trip in km/h?
4 m
DST triangle Average speed Journey by parts Different speed Same starting point Same starting time Common time
231 P6.SP.TL.18012288
Level 3
Andy and Benny were planning to run on a circular track with a circumference of 400 m. Both of them started jogging together at the same start point and moved round the track in a clockwise direction at uniform speeds. Andy completed a full round in 50 s. Benny completed a full round in 40 s.
  1. How long would it take for Benny to overtake Andy for the first time?
  2. How far was Benny ahead of Andy after 10 s?
4 m
DST triangle Same starting point Distance apart Overtaking Circular track Duration LCM
232 P6.AN.NK.17051721
Level 3
The figure is not drawn to scale. UVY is an equilateral triangle and XVW is an isosceles triangle. WVU and VXZ are straight lines and WU//ZY. ∠YVZ = 90° and ∠XYV = 56°.
  1. Find ∠WVZ.
  2. Find ∠VXW.
  3. Find ∠YXZ.
4 m
Equilateral triangle Isosceles triangle Angles on a straight line
233 P6.AP.TL.17090815
Level 3
The figure, not drawn to scale, is made up of two identical right-angled triangles, a small square and a big square. The lengths of the 2 squares are whole numbers. The perimeter of the shaded region is 32 cm, and the total area of the two unshaded squares is 89 cm2. Find the total area of the two shaded right-angled triangles.
3 m
Square Right-angled triangle Composite figure perimeter Composite figure area Guess & check
234 P6.SP.TL.18012289
Level 3
Shan and Ella started off at the same spot and ran at average speeds round a 3-km circular path. Shan took 15 minutes to complete each round. Ella completed each round in 20 minutes.
  1. How far ahead of Ella would Shan be after 1 minute? Express the answer in metres.
  2. How long would it take Shan to meet Ella for the first time?
  3. How many rounds would Shan have completed by then?
4 m
DST triangle Same starting point Meeting point Distance apart Circular track Unit conversion Duration LCM
235 P6.AN.NK.17051740
Level 3
The figure is not drawn to scale. BCEF is a square and ABF is an equilateral triangle. CDE is an isosceles triangle. AED is a straight line.
  1. Find ∠FAE.
  2. Find ∠CDE.
4 m
Square Equilateral triangle Isosceles triangle Angles on a straight line
236 P6.AN.NK.17051754
Level 3
In the figure, not drawn to scale, PQRS is a square. RLN, SLQ and RMN are straight lines. Find the value of ∠PMN.
4 m
Right angle Square Vertically opposite angles Angles sum of triangle
237 P6.AN.NK.17051701
Level 3
The figure is not drawn to scale. Triangle ABZ is an isosceles triangle. Triangle XYZ is an equilateral triangle. ∠BZA is 15 of ∠YXZ and ∠YZB = ∠XZA.
  1. Find ∠YZB.
  2. Find ∠XAZ.
4 m
Equilateral triangle Isosceles triangle Angles sum of triangle Fraction of a whole
238 P6.AN.NK.17081805
Level 3 PSLE
In the diagram, XLP and YMN are equilateral triangles. WXYZ is a straight line. ∠ZYN = 62° and ∠WXL = 92°. Find ∠a.
4 m
Equilateral triangle Angles on a straight line Vertically opposite angles Angles sum of triangle
239 P6.AN.NK.17051731
Level 3
The figure, not drawn to scale, is made up of an isosceles triangle and a rhombus. ∠c = ∠b, ∠a is twice ∠d, ∠b is twice ∠e and ∠c is less than ∠e by 51°.
  1. Find ∠c.
  2. Find the difference between ∠a and ∠c.
4 m
Isosceles triangle Rhombus Angles sum of triangle More than or less than Times as many Units
240 P6.AN.NK.21060916
Level 3 PSLE
In the figure, ABFG is a parallelogram and CDEF is a rhombus. GFE is a straight line. ∠BAG = 53°, ∠FBC = 27° and ∠DCE = 35°.
  1. Find ∠BFC.
  2. Find ∠BCD.
4 m
Isosceles triangle Parallelogram Rhombus Angles on a straight line Angles sum of triangle Angles at a point

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