Daily Practice · Higher Plus
September 1995 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1995 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1995
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1995Rationalise the denominator of 12/sqrt(3), giving your answer in its simplest form.
- 2nd September 1995f(x) = 5x - 11. Work out the inverse function f^-1(x).
- 3rd September 1995y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 25.
- 4th September 1995The 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.
- 5th September 1995A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 7/15. Work out r.
- 6th September 1995On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 7th September 1995Simplify sqrt(18) + sqrt(98), giving your answer in the form a sqrt(b).
- 8th September 1995Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.
- 9th September 1995A train slows steadily from 15 m/s to rest in 10 seconds. Work out its deceleration.
- 10th September 1995In 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.
- 11th September 1995The probability of winning a game is 7/10. A player expects 63 wins. How many games did they play?
- 12th September 1995A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 3.5. How many values in total?
- 13th September 1995A rectangle is 11 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 14th September 1995Use the iteration x(n+1) = cube root of (9x(n) + 8) with x(0) = 2. Work out x(1) to 3 decimal places.
- 15th September 1995y is inversely proportional to x^2. When x = 3, y = 100. Work out y when x = 5.
- 16th September 1995In a vector proof you find that vector PQ = 6a + 5b and vector RS = 30a + 25b. What does this show about PQ and RS?
- 17th September 1995A bag holds 4 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 18th September 1995On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 19th September 1995Expand and simplify (7 + sqrt(3))(7 - sqrt(3)).
- 20th September 1995Work out the nth term of the quadratic sequence 5, 7, 13, 23, ...
- 21st September 1995y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
- 22nd September 1995A cuboid measures 15 cm by 10 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd September 1995A 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?
- 24th September 1995A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 1.4. How many values in total?
- 25th September 1995A block has mass 340 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 26th September 1995The point (6, 2) lies on y = f(x). Write down its image on y = f(x) - 6.
- 27th September 1995y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 36.
- 28th September 1995A cuboid measures 14 cm by 5 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th September 1995A bag holds 4 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th September 1995On 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?