Daily Practice · Higher Plus
July 1999 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 1999, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 1999 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1999
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1999Simplify (x^2 - x - 2)/(x - 2).
- 2nd July 1999A train slows steadily from 27 m/s to rest in 10 seconds. Work out its deceleration.
- 3rd July 1999A cuboid measures 4 cm by 9 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th July 1999A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th July 1999A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 0.8. How many values in total?
- 6th July 1999Expand and simplify (3 + sqrt(10))(3 - sqrt(10)).
- 7th July 1999In an algebraic proof, how would you write a multiple of 9 in terms of an integer n?
- 8th July 1999y is inversely proportional to x^2. When x = 4, y = 16. Work out y when x = 2.
- 9th July 1999A cuboid measures 13 cm by 10 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th July 1999A bag holds 4 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th July 1999On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 12th July 1999A block has mass 520 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 13th July 1999Make x the subject of 7x + 8 = y(x + 8).
- 14th July 1999y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 15th July 1999The 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.
- 16th July 1999A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/21. Work out r.
- 17th July 1999A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 3.5. How many values in total?
- 18th July 1999x = 105 and y = 13, each correct to the nearest whole number. Work out the upper bound of x - y.
- 19th July 1999Write 2/(x - 5) + 5/(x + 1) as a single fraction.
- 20th July 1999y is directly proportional to sqrt(x). When x = 49, y = 28. Work out y when x = 16.
- 21st July 1999In 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.
- 22nd July 1999The probability of winning a game is 4/5. A player expects 8 wins. How many games did they play?
- 23rd July 1999On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 24th July 1999A car covers 900 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 25th July 1999Solve 6x^2 - x - 2 = 0.
- 26th July 1999A train slows steadily from 18 m/s to rest in 8 seconds. Work out its deceleration.
- 27th July 1999In a vector proof you find that vector PQ = 3a + 6b and vector RS = 9a + 18b. What does this show about PQ and RS?
- 28th July 1999A bag holds 2 red and n blue counters. The probability of taking a red is 2/7. Work out n.
- 29th July 1999A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 1.4. How many values in total?
- 30th July 1999Rationalise the denominator of 18/sqrt(3), giving your answer in its simplest form.
- 31st July 1999f(x) = 2x + 7. Work out the inverse function f^-1(x).