Daily Practice · Higher Plus
February 1996 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' February 1996 sheets in a single PDF, each tier behind its own divider page - 145 sheets in one file.
Every sheet in February 1996
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1996The 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.
- 2nd February 1996A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 3rd February 1996A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 0.8. How many values in total?
- 4th February 1996x = 90 and y = 77, each correct to the nearest whole number. Work out the upper bound of x - y.
- 5th February 1996Solve x^2 + 9x + 8 < 0.
- 6th February 1996y is inversely proportional to x^2. When x = 4, y = 27. Work out y when x = 3.
- 7th February 1996In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 8th February 1996The probability of winning a game is 1/10. A player expects 10 wins. How many games did they play?
- 9th February 1996On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 10th February 1996A car covers 320 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 11th February 1996Write x^2 - 14x - 2 in the form (x + a)^2 + b.
- 12th February 1996y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 4.
- 13th February 1996In a vector proof you find that vector PQ = 3a - 6b and vector RS = 12a - 24b. What does this show about PQ and RS?
- 14th February 1996A bag holds 4 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 15th February 1996A histogram has two bars: one 5 units wide with frequency density 1.5, one 5 units wide with density 1.4. How many values in total?
- 16th February 1996Rationalise the denominator of 63/sqrt(7), giving your answer in its simplest form.
- 17th February 1996Work out the coordinates of the turning point of y = x^2 - 14x - 7.
- 18th February 1996y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 81.
- 19th February 1996A cuboid measures 8 cm by 3 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th February 1996A bag holds 6 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st February 1996On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 22nd February 1996Simplify sqrt(18) + sqrt(98), giving your answer in the form a sqrt(b).
- 23rd February 1996Simplify (x^2 - 8x + 12)/(x - 2).
- 24th February 1996A train slows steadily from 29 m/s to rest in 8 seconds. Work out its deceleration.
- 25th February 1996A cuboid measures 11 cm by 6 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th February 1996A bag holds 6 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th February 1996A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 1.4. How many values in total?
- 28th February 1996A rectangle is 21 cm by 7 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 29th February 1996In an algebraic proof, how would you write two consecutive odd numbers in terms of an integer n?