Daily Practice · Higher Plus
June 1996 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' June 1996 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1996
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1996A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 2nd June 1996A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
- 3rd June 1996A block has mass 250 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 4th June 1996Simplify (x^2 + 5x - 6)/(x - 1).
- 5th June 1996y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
- 6th June 1996In 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.
- 7th June 1996The probability of winning a game is 1/5. A player expects 4 wins. How many games did they play?
- 8th June 1996On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 9th June 1996x = 86 and y = 50, each correct to the nearest whole number. Work out the upper bound of x - y.
- 10th June 1996In an algebraic proof, how would you write the number two more than an even number in terms of an integer n?
- 11th June 1996y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
- 12th June 1996In a vector proof you find that vector PQ = 5a + 4b and vector RS = 25a + 20b. What does this show about PQ and RS?
- 13th June 1996A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
- 14th June 1996A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 1.4. How many values in total?
- 15th June 1996A car covers 470 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.
- 16th June 1996Make x the subject of 5x + 8 = y(x + 8).
- 17th June 1996y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 49.
- 18th June 1996A cuboid measures 6 cm by 3 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 19th June 1996A bag holds 8 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 20th June 1996On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 21st June 1996Rationalise the denominator of 48/sqrt(6), giving your answer in its simplest form.
- 22nd June 1996Write 7/(x + 6) + 3/(x - 1) as a single fraction.
- 23rd June 1996A train slows steadily from 29 m/s to rest in 8 seconds. Work out its deceleration.
- 24th June 1996A cuboid measures 6 cm by 5 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 25th June 1996A bag holds 4 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 26th June 1996A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 0.8. How many values in total?
- 27th June 1996Simplify sqrt(20) + sqrt(80), giving your answer in the form a sqrt(b).
- 28th June 1996Solve 15x^2 + 28x + 5 = 0.
- 29th June 1996y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 6.
- 30th June 1996The 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.