Daily Practice · Higher Plus
September 1996 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1996 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1996
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1996x = 87 and y = 60, each correct to the nearest whole number. Work out the upper bound of x - y.
- 2nd September 1996Write x^2 - 4x - 10 in the form (x + a)^2 + b.
- 3rd September 1996A train slows steadily from 15 m/s to rest in 5 seconds. Work out its deceleration.
- 4th September 1996In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 5th September 1996The probability of winning a game is 3/4. A player expects 33 wins. How many games did they play?
- 6th September 1996A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 0.8. How many values in total?
- 7th September 1996A car covers 250 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 8th September 1996Work out the coordinates of the turning point of y = x^2 + 14x + 13.
- 9th September 1996y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 6.
- 10th September 1996In a vector proof you find that vector PQ = 3a - 5b and vector RS = 12a - 20b. What does this show about PQ and RS?
- 11th September 1996A bag holds 6 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 12th September 1996On 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?
- 13th September 1996Rationalise the denominator of 56/sqrt(7), giving your answer in its simplest form.
- 14th September 1996Simplify (x^2 - 3x - 4)/(x - 4).
- 15th September 1996y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 5.
- 16th September 1996A cuboid measures 10 cm by 8 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th September 1996A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th September 1996A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
- 19th September 1996Simplify sqrt(45) + sqrt(5), giving your answer in the form a sqrt(b).
- 20th September 1996In an algebraic proof, how would you write the number two more than an even number in terms of an integer n?
- 21st September 1996y is directly proportional to sqrt(x). When x = 4, y = 10. Work out y when x = 64.
- 22nd September 1996A cuboid measures 11 cm by 8 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd September 1996A bag holds 7 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th September 1996On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 25th September 1996A rectangle is 27 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 26th September 1996Make x the subject of 8x + 2 = y(x + 2).
- 27th September 1996A train slows steadily from 38 m/s to rest in 5 seconds. Work out its deceleration.
- 28th September 1996The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 29th September 1996A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 30th September 1996A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 3.5. How many values in total?