Daily Practice · Higher Plus
June 2003 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2003, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2003 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2003
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2003The probability of winning a game is 1/4. A player expects 24 wins. How many games did they play?
- 2nd June 2003A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 3. How many values in total?
- 3rd June 2003Expand and simplify (8 + sqrt(5))(8 - sqrt(5)).
- 4th June 2003In an algebraic proof, how would you write a multiple of 7 in terms of an integer n?
- 5th June 2003y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 25.
- 6th June 2003In a vector proof you find that vector PQ = 5a + 2b and vector RS = 25a + 10b. What does this show about PQ and RS?
- 7th June 2003A bag holds 8 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 8th June 2003On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 9th June 2003A block has mass 320 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 10th June 2003Make x the subject of 4x + 3 = y(x + 3).
- 11th June 2003A train slows steadily from 33 m/s to rest in 8 seconds. Work out its deceleration.
- 12th June 2003A cuboid measures 15 cm by 8 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 13th June 2003A bag holds 3 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 14th June 2003A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 3. How many values in total?
- 15th June 2003x = 32 and y = 20, each correct to the nearest whole number. Work out the upper bound of x - y.
- 16th June 2003Write 3/(x + 2) + 5/(x + 4) as a single fraction.
- 17th June 2003y is inversely proportional to x^2. When x = 5, y = 144. Work out y when x = 6.
- 18th June 2003A cuboid measures 5 cm by 7 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 19th June 2003A bag holds 6 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 20th June 2003On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 21st June 2003A car covers 170 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 22nd June 2003Solve 12x^2 - 35x + 25 = 0.
- 23rd June 2003y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
- 24th June 2003The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 25th June 2003A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 15/22. Work out r.
- 26th June 2003A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
- 27th June 2003Rationalise the denominator of 21/sqrt(7), giving your answer in its simplest form.
- 28th June 2003f(x) = 6x - 2. Work out the inverse function f^-1(x).
- 29th June 2003y is directly proportional to sqrt(x). When x = 36, y = 12. Work out y when x = 16.
- 30th June 2003In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.