Daily Practice · Higher Plus
October 1995 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1995 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1995
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1995x = 179 and y = 134, each correct to the nearest whole number. Work out the upper bound of x - y.
- 2nd October 1995Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 3rd October 1995A train slows steadily from 33 m/s to rest in 8 seconds. Work out its deceleration.
- 4th October 1995The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 5th October 1995A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 6th October 1995A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 0.8. How many values in total?
- 7th October 1995A car covers 690 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 8th October 1995f(x) = 5x + 7 and g(x) = 6x + 2. Work out fg(2).
- 9th October 1995y is inversely proportional to x^2. When x = 3, y = 32. Work out y when x = 4.
- 10th October 1995In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 11th October 1995The probability of winning a game is 9/10. A player expects 99 wins. How many games did they play?
- 12th October 1995On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 13th October 1995Rationalise the denominator of 63/sqrt(7), giving your answer in its simplest form.
- 14th October 1995The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 15th October 1995y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
- 16th October 1995In a vector proof you find that vector PQ = 3a - 2b and vector RS = 6a - 4b. What does this show about PQ and RS?
- 17th October 1995A bag holds 8 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 18th October 1995A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 3.5. How many values in total?
- 19th October 1995Simplify sqrt(80) + sqrt(245), giving your answer in the form a sqrt(b).
- 20th October 1995A quadratic sequence starts 15, 23, 33, 45. Work out the second difference, and the coefficient of n^2.
- 21st October 1995y is directly proportional to sqrt(x). When x = 49, y = 28. Work out y when x = 16.
- 22nd October 1995A cuboid measures 14 cm by 13 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd October 1995A bag holds 5 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th October 1995On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 25th October 1995A rectangle is 8 cm by 9 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 26th October 1995Solve x^2 - 14x + 33 > 0.
- 27th October 1995A train slows steadily from 17 m/s to rest in 5 seconds. Work out its deceleration.
- 28th October 1995A cuboid measures 6 cm by 11 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th October 1995A bag holds 6 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th October 1995A 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?
- 31st October 1995Expand and simplify (2 + sqrt(7))(2 - sqrt(7)).