Daily Practice · Higher Plus
September 1985 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1985 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1985
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1985y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 2nd September 1985In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 3rd September 1985The probability of winning a game is 4/5. A player expects 40 wins. How many games did they play?
- 4th September 1985A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 3.5. How many values in total?
- 5th September 1985Simplify sqrt(32) + sqrt(18), giving your answer in the form a sqrt(b).
- 6th September 1985The point (2, 0) lies on y = f(x). Write down its image on y = f(x - 2).
- 7th September 1985y is directly proportional to sqrt(x). When x = 9, y = 6. Work out y when x = 36.
- 8th September 1985In a vector proof you find that vector PQ = 2a + b and vector RS = 6a + 3b. What does this show about PQ and RS?
- 9th September 1985A bag holds 4 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 10th September 1985On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 11th September 1985A rectangle is 20 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 12th September 1985Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 13th September 1985A train slows steadily from 23 m/s to rest in 8 seconds. Work out its deceleration.
- 14th September 1985A cuboid measures 5 cm by 5 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 15th September 1985A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 16th September 1985A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 0.6. How many values in total?
- 17th September 1985Expand and simplify (6 + sqrt(7))(6 - sqrt(7)).
- 18th September 1985f(x) = 4x + 9 and g(x) = 3x + 3. Work out fg(2).
- 19th September 1985y is inversely proportional to x^2. When x = 5, y = 18. Work out y when x = 3.
- 20th September 1985A cuboid measures 9 cm by 7 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 21st September 1985A bag holds 7 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 22nd September 1985On 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?
- 23rd September 1985A block has mass 520 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 24th September 1985The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 25th September 1985y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 4.
- 26th September 1985The 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.
- 27th September 1985A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 28th September 1985A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 29th September 1985x = 158 and y = 118, each correct to the nearest whole number. Work out the upper bound of x - y.
- 30th September 1985A quadratic sequence starts 13, 34, 65, 106. Work out the second difference, and the coefficient of n^2.