Daily Practice · Higher Plus
February 2006 - Higher Plus 5-a-day
Every Higher Plus sheet published in February 2006, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' February 2006 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 2006
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 2006y is inversely proportional to x^2. When x = 3, y = 32. Work out y when x = 4.
- 2nd February 2006A cuboid measures 11 cm by 8 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd February 2006A bag holds 4 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th February 2006On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 5th February 2006x = 159 and y = 26, each correct to the nearest whole number. Work out the upper bound of x - y.
- 6th February 2006f(x) = 2x + 3 and g(x) = 4x - 3. Work out fg(1).
- 7th February 2006y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.
- 8th February 2006The 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.
- 9th February 2006A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/22. Work out r.
- 10th February 2006A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 1.4. How many values in total?
- 11th February 2006A car covers 270 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 12th February 2006The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 13th February 2006y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 4.
- 14th February 2006In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 15th February 2006The probability of winning a game is 3/4. A player expects 15 wins. How many games did they play?
- 16th February 2006On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 17th February 2006Rationalise the denominator of 50/sqrt(5), giving your answer in its simplest form.
- 18th February 2006A quadratic sequence starts 10, 21, 42, 73. Work out the second difference, and the coefficient of n^2.
- 19th February 2006A train slows steadily from 32 m/s to rest in 4 seconds. Work out its deceleration.
- 20th February 2006In a vector proof you find that vector PQ = 2a + 3b and vector RS = 6a + 9b. What does this show about PQ and RS?
- 21st February 2006A bag holds 7 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 22nd February 2006A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
- 23rd February 2006Simplify sqrt(50) + sqrt(18), giving your answer in the form a sqrt(b).
- 24th February 2006Solve x^2 - 3x + 2 < 0.
- 25th February 2006y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.
- 26th February 2006A cuboid measures 15 cm by 13 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th February 2006A bag holds 7 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 28th February 2006On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?