Daily Practice · Higher Plus
June 1999 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 1999, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 1999 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1999
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1999The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 2nd June 1999y is directly proportional to sqrt(x). When x = 25, y = 15. Work out y when x = 9.
- 3rd June 1999A cuboid measures 6 cm by 10 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th June 1999A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th June 1999On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 6th June 1999x = 159 and y = 57, each correct to the nearest whole number. Work out the upper bound of x - y.
- 7th June 1999A quadratic sequence starts 5, 19, 41, 71. Work out the second difference, and the coefficient of n^2.
- 8th June 1999A train slows steadily from 12 m/s to rest in 5 seconds. Work out its deceleration.
- 9th June 1999A cuboid measures 12 cm by 12 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th June 1999A bag holds 7 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th June 1999A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 12th June 1999A car covers 790 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 13th June 1999Solve x^2 + 2x - 8 > 0.
- 14th June 1999y is inversely proportional to x^2. When x = 3, y = 25. Work out y when x = 5.
- 15th June 1999The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 16th June 1999A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 17th June 1999On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 18th June 1999Rationalise the denominator of 12/sqrt(6), giving your answer in its simplest form.
- 19th June 1999Write x^2 + 14x + 11 in the form (x + a)^2 + b.
- 20th June 1999y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 5.
- 21st June 1999In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 22nd June 1999The probability of winning a game is 1/5. A player expects 8 wins. How many games did they play?
- 23rd June 1999A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
- 24th June 1999Simplify sqrt(72) + sqrt(72), giving your answer in the form a sqrt(b).
- 25th June 1999Work out the coordinates of the turning point of y = x^2 - 10x - 13.
- 26th June 1999y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 36.
- 27th June 1999In a vector proof you find that vector PQ = 3a - b and vector RS = 15a - 5b. What does this show about PQ and RS?
- 28th June 1999A bag holds 4 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 29th June 1999On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 30th June 1999A rectangle is 21 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.