Daily Practice · Higher Plus
July 1992 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' July 1992 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1992
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1992Work out the coordinates of the turning point of y = x^2 - 6x + 4.
- 2nd July 1992y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
- 3rd July 1992In a vector proof you find that vector PQ = 3a + 2b and vector RS = 15a + 10b. What does this show about PQ and RS?
- 4th July 1992A bag holds 8 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 5th July 1992A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 6th July 1992A block has mass 300 g (to the nearest 10 g) and volume 9 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 7th July 1992Simplify (x^2 + 9x + 18)/(x + 6).
- 8th July 1992y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 4.
- 9th July 1992A cuboid measures 8 cm by 13 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th July 1992A bag holds 5 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th July 1992On 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?
- 12th July 1992x = 101 and y = 91, each correct to the nearest whole number. Work out the upper bound of x - y.
- 13th July 1992In an algebraic proof, how would you write the next odd number after 2n + 1 in terms of an integer n?
- 14th July 1992A train slows steadily from 23 m/s to rest in 10 seconds. Work out its deceleration.
- 15th July 1992A cuboid measures 14 cm by 5 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th July 1992A bag holds 7 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th July 1992A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
- 18th July 1992A car covers 760 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 19th July 1992Make x the subject of 4x + 4 = y(x + 4).
- 20th July 1992y is inversely proportional to x^2. When x = 2, y = 108. Work out y when x = 6.
- 21st July 1992The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 22nd July 1992A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/3. Work out r.
- 23rd July 1992On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 24th July 1992Rationalise the denominator of 12/sqrt(2), giving your answer in its simplest form.
- 25th July 1992Write 7/(x - 6) + 7/(x - 1) as a single fraction.
- 26th July 1992y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 27th July 1992In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 28th July 1992The probability of winning a game is 5/8. A player expects 65 wins. How many games did they play?
- 29th July 1992A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
- 30th July 1992Simplify sqrt(72) + sqrt(2), giving your answer in the form a sqrt(b).
- 31st July 1992Solve 15x^2 + 34x + 15 = 0.