Daily Practice · Higher Plus
June 1998 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 1998, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 1998 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1998
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1998y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 5.
- 2nd June 1998In a vector proof you find that vector PQ = 5a + 2b and vector RS = 25a + 10b. What does this show about PQ and RS?
- 3rd June 1998A bag holds 6 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 4th June 1998A histogram has two bars: one 5 units wide with frequency density 1.5, one 5 units wide with density 0.6. How many values in total?
- 5th June 1998Rationalise the denominator of 84/sqrt(7), giving your answer in its simplest form.
- 6th June 1998Write 6/(x - 4) + 7/(x - 3) as a single fraction.
- 7th June 1998y is directly proportional to sqrt(x). When x = 9, y = 12. Work out y when x = 49.
- 8th June 1998A cuboid measures 9 cm by 3 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th June 1998A bag holds 6 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 10th June 1998On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 11th June 1998Simplify sqrt(18) + sqrt(8), giving your answer in the form a sqrt(b).
- 12th June 1998Solve 12x^2 - 13x + 3 = 0.
- 13th June 1998A train slows steadily from 22 m/s to rest in 4 seconds. Work out its deceleration.
- 14th June 1998A cuboid measures 8 cm by 11 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 15th June 1998A bag holds 3 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th June 1998A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 17th June 1998A rectangle is 15 cm by 16 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 18th June 1998f(x) = 2x + 8. Work out the inverse function f^-1(x).
- 19th June 1998y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 6.
- 20th June 1998The 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.
- 21st June 1998A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 6/55. Work out r.
- 22nd June 1998On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 23rd June 1998Expand and simplify (2 + sqrt(7))(2 - sqrt(7)).
- 24th June 1998Solve x^2 + y^2 = 841 and y = x + 1 simultaneously.
- 25th June 1998y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 26th June 1998In 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.
- 27th June 1998The probability of winning a game is 1/2. A player expects 4 wins. How many games did they play?
- 28th June 1998A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 1.4. How many values in total?
- 29th June 1998A block has mass 500 g (to the nearest 10 g) and volume 21 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 30th June 1998Use the iteration x(n+1) = cube root of (11x(n) + 3) with x(0) = 4. Work out x(1) to 3 decimal places.