Daily Practice · Higher Plus
November 1992 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' November 1992 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1992
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 1992A bag holds 5 red and n blue counters. The probability of taking a red is 5/12. Work out n.
- 2nd November 1992A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 3. How many values in total?
- 3rd November 1992Expand and simplify (3 + sqrt(2))(3 - sqrt(2)).
- 4th November 1992Write 5/(x + 5) + 7/(x + 6) as a single fraction.
- 5th November 1992y is directly proportional to sqrt(x). When x = 9, y = 9. Work out y when x = 36.
- 6th November 1992A cuboid measures 7 cm by 4 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th November 1992A bag holds 3 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 8th November 1992On 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 November 1992A block has mass 360 g (to the nearest 10 g) and volume 15 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 10th November 1992Solve 16x^2 - 16x + 3 = 0.
- 11th November 1992A train slows steadily from 16 m/s to rest in 10 seconds. Work out its deceleration.
- 12th November 1992A cuboid measures 9 cm by 10 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th November 1992A bag holds 4 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th November 1992A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 0.8. How many values in total?
- 15th November 1992x = 86 and y = 65, each correct to the nearest whole number. Work out the upper bound of x - y.
- 16th November 1992f(x) = 8x + 5. Work out the inverse function f^-1(x).
- 17th November 1992y is inversely proportional to x^2. When x = 4, y = 12. Work out y when x = 2.
- 18th November 1992The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 19th November 1992A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 20th November 1992On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 21st November 1992A car covers 250 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 22nd November 1992Solve x^2 + y^2 = 225 and y = x - 3 simultaneously.
- 23rd November 1992y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
- 24th November 1992In 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.
- 25th November 1992The probability of winning a game is 5/8. A player expects 40 wins. How many games did they play?
- 26th November 1992A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 1.4. How many values in total?
- 27th November 1992Rationalise the denominator of 6/sqrt(3), giving your answer in its simplest form.
- 28th November 1992Use the iteration x(n+1) = cube root of (3x(n) + 5) with x(0) = 5. Work out x(1) to 3 decimal places.
- 29th November 1992y is directly proportional to sqrt(x). When x = 25, y = 30. Work out y when x = 36.
- 30th November 1992In a vector proof you find that vector PQ = 2a + b and vector RS = 4a + 2b. What does this show about PQ and RS?