Daily Practice · Higher Plus
September 1992 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1992 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1992
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1992In a vector proof you find that vector PQ = a + 5b and vector RS = 4a + 20b. What does this show about PQ and RS?
- 2nd September 1992A bag holds 7 red and n blue counters. The probability of taking a red is 7/15. Work out n.
- 3rd September 1992A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 4th September 1992Rationalise the denominator of 14/sqrt(7), giving your answer in its simplest form.
- 5th September 1992Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 6th September 1992y is inversely proportional to x^2. When x = 5, y = 9. Work out y when x = 3.
- 7th September 1992A cuboid measures 15 cm by 9 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th September 1992A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 9th September 1992On 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?
- 10th September 1992Simplify sqrt(12) + sqrt(108), giving your answer in the form a sqrt(b).
- 11th September 1992f(x) = 2x - 4 and g(x) = 5x - 6. Work out fg(6).
- 12th September 1992y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
- 13th September 1992A cuboid measures 4 cm by 6 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th September 1992A bag holds 7 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th September 1992A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 16th September 1992A rectangle is 22 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 17th September 1992The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 18th September 1992y is directly proportional to sqrt(x). When x = 36, y = 18. Work out y when x = 64.
- 19th September 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.
- 20th September 1992A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 21st September 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?
- 22nd September 1992Expand and simplify (7 + sqrt(7))(7 - sqrt(7)).
- 23rd September 1992A quadratic sequence starts 10, 17, 26, 37. Work out the second difference, and the coefficient of n^2.
- 24th September 1992A train slows steadily from 13 m/s to rest in 10 seconds. Work out its deceleration.
- 25th September 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.
- 26th September 1992The probability of winning a game is 1/5. A player expects 24 wins. How many games did they play?
- 27th September 1992A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 3.5. How many values in total?
- 28th September 1992A block has mass 620 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 29th September 1992Solve x^2 + 14x + 48 > 0.
- 30th September 1992y is inversely proportional to x^2. When x = 2, y = 25. Work out y when x = 5.