Daily Practice · Higher Plus
May 2003 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 2003, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 2003 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 2003
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 2003In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 2nd May 2003The probability of winning a game is 3/5. A player expects 30 wins. How many games did they play?
- 3rd May 2003On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4th May 2003x = 174 and y = 29, each correct to the nearest whole number. Work out the upper bound of x - y.
- 5th May 2003A quadratic sequence starts 12, 22, 38, 60. Work out the second difference, and the coefficient of n^2.
- 6th May 2003y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
- 7th May 2003In a vector proof you find that vector PQ = 4a + b and vector RS = 8a + 2b. What does this show about PQ and RS?
- 8th May 2003A bag holds 3 red and n blue counters. The probability of taking a red is 3/10. Work out n.
- 9th May 2003A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 3.5. How many values in total?
- 10th May 2003A car covers 330 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 11th May 2003Solve x^2 + 10x + 21 < 0.
- 12th May 2003y is directly proportional to sqrt(x). When x = 25, y = 10. Work out y when x = 49.
- 13th May 2003A cuboid measures 13 cm by 7 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th May 2003A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 15th May 2003On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 16th May 2003Rationalise the denominator of 54/sqrt(6), giving your answer in its simplest form.
- 17th May 2003Write x^2 + 12x - 5 in the form (x + a)^2 + b.
- 18th May 2003A train slows steadily from 26 m/s to rest in 5 seconds. Work out its deceleration.
- 19th May 2003A cuboid measures 11 cm by 10 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th May 2003A bag holds 6 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st May 2003A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 0.6. How many values in total?
- 22nd May 2003Simplify sqrt(27) + sqrt(147), giving your answer in the form a sqrt(b).
- 23rd May 2003Work out the coordinates of the turning point of y = x^2 + 6x - 3.
- 24th May 2003y is inversely proportional to x^2. When x = 4, y = 25. Work out y when x = 5.
- 25th May 2003The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 26th May 2003A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 27th May 2003On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 28th May 2003A rectangle is 21 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 29th May 2003Simplify (x^2 - 7x - 8)/(x + 1).
- 30th May 2003y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
- 31st May 2003In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.